Two new rides are being compared by a local amuse-ment

Electricity is sold for $0.12 per kilowatt-hour(kWh) for the first 10,000 units each month and$0.09/kWh for all remaining units. If a firm uses14,000kWh/month, what is its average and marginalcost?

One of your firms suppliers discounts prices forlarger quantities. The first1000 parts are $13 each.The next 2000 are $12 each. All parts in excess of3000 cost $11 each. What are the average cost andmarginal cost per part for the following quantities?(a)500(b)1500(c)2500(d)3500

A new machine comes with 100 free service hoursover the first year. Additional time costs $75 per hour.What are the average and marginal costs per hour forthe following quantities?(a)75(b)125(c)250

Venus Computer can produce 23,000 personal com-puters a year on its daytime shift. The fixed manu-facturing costs per year are $2 million and the totallabor cost is $9,109,000. To increase its productionto 46,000 computers per year, Venus is consideringadding a second shift. The unit labor cost for the sec-ond shift would be 25% higher than the day shift,but the totalfixed manufacturingcostswouldincreaseonly to $2.4 million from $2 million.(a)Compute the unit manufacturing cost for the day-time shift.(b)Would adding a second shift increase or decreasethe unit manufacturing cost at the plant?

A small machine shop, with 30 hp of connectedload, purchases electricity at the following monthlyrates (assume any demand charge is included in thisschedule) per hp of connected load:First 50 kWh at 12.6?cperkWhNext 50 kWh at 10.6?cperkWhNext 150 kWh at 6.0?cperkWhOver 250 kWh at 5.7?cperkWhThe shop uses 2800 kWh per month.(a)Calculate the monthly bill for this shop.What are the marginal and average costs perkilowatt-hour?(b)Suppose Jennifer, the proprietor of the shop,has the chance to secure additional business thatwill require her to operate her existing equip- ment more hours per day. This will use an extra1200 kWh per month. What is the lowest figurethat she might reasonably consider to be thecost of this additional energy? What is this perkilowatt- hour?(c)Jennifer contemplates installing certain newmachines that will reduce the labor time requiredon certain operations. These will increase theconnectedload by 10 hp, but since they will oper-ate only on certain special jobs, will add only100 kWh per month. In a study to determine theeconomy of installing these new machines, whatshould be consideredas the cost of this energy?What is this per kilowatt-hour?

Two automatic systems for dispensing maps arebeing compared by the state highway department.The accompanying breakeven chart of the compari-son of these systems (System I vs. System II) showstotal yearly costs for the number of maps dispensedper year for both alternatives. Answer the followingquestions.(a)What is the fixed cost for System I?(b)What is the fixed cost for System II?(c)What is the variable cost per map dispensed forSystem I?(d)What is the variable cost per map dispensed forSystem II?(e)What is the breakeven point in terms of mapsdispensed at which the two systems have equalannual costs?(f)For what range of annual number of maps dis-pensed is System I recommended?(g)For what range of annual number of maps dis-pensed is System II recommended?(h)At 3000 maps per year,what are the marginal andaverage map costs for each system?

A privately owned summer camp for youngsters hasthe following data for a 12-week session:Charge per camper$480 per weekFixed costs$192,000 per sessionVariable cost per camper$320 per weekCapacity200 campers(a)Develop the mathematical relationships for totalcost and total revenue.(b)What is the total number of campers that willallow the camp tojust break even?(c)What is the profit or loss for the 12-week sessionif the camp operates at 80% capacity?(d)What are marginal and average costs per camperat 80% capacity?

Two new rides are being compared by a local amuse-ment park in terms of their annual operating costs.The two rides are assumed to be able to generatethe same level of revenue (thus the focus on costs).The Tummy Tugger has fixed costs of $10,000 peryear and variable costs of $2.50 per visitor. The HeadBuzzer has fixed costs of $4000 per year and variablecosts of $4 per visitor. Provide answers to the follow-ing questions so the amusement park can make theneeded comparison.(a)Mathematically determine the breakeven numberof visitors per year for the two rides to have equalannual costs.(b)Develop a breakeven graph that illustrates thefollowing:Accurate total cost lines for the two alterna-tives (show line, slopes, and equations).The breakeven point for the two rides in termsof number of visitors.The ranges of visitors per year where eachalternative is preferred.

Consider the accompanying breakeven graph for aninvestment, and answer the following questions. a)Give the equation for total revenue forxunits peryear.(b)Give the equation for total costs forxunits peryear.(c)What is the breakeven level ofx?(d)If you sell 1500 units this year, will you have aprofit or loss? How much?(e)At 1500 units, what are your marginal and aver-age costs?

Quatro Hermanas, Inc. is investigating implement-ing some new production machinery as part of itsoperations. Three alternatives have been identified,and they have the following fixed and variable costs Determine the ranges of production (units producedper year) over which each alternative would be rec-ommended up to 30,000 units per year.

Three alternative designs have been created bySnakisco engineers for a new machine that spreadscheesebetween the crackersin a Snakiscosnack.Thecosts for the three designs (wherexis the annualproduction rate of boxes of cheese crackers) follow: a)Managementis interested in the production inter-val of 0150,000 boxes of crackers per year.Mathematically determine the production vol-ume over which each design (AorBorC) wouldbe chosen.(b)Depict your solution from part (a) graphically,clearly labeling youraxes and including atitleforthe graph, so that management can easily see thefollowing:i.Accurate total cost lines for each alternative(show line, slopes, and line equations).ii.Any relevantbreakeven,orcrossoverpoints.iii.Ranges of annual production where eachalternative is preferred

A painting operation is performed by a productionworkerata laborcostof$1.40 perunit. A robotspray- painting machine, costing $15,000, would reducethe labor cost to $0.20 per unit. If the device wouldbe valueless at the end of 3 years, what is theminimum number of units that would have to bepainted each year to justify the purchase of the robotmachine?

CompanyAhas fixed expenses of $15,000 per yearand each unit of product has a $0.20 variable cost.CompanyBhas fixed expenses of $5000 per yearand can produce the same product at a $0.50 variablecost. At what number of units of annual produc-tion will CompanyAhave the same overall cost asCompanyB?

Mr. Sam Spade, the president of Ajax, recently readin a report that a competitor named Bendix has thefollowing relationship between cost and productionquantity:C=$3,000,000$18,000Q+$75Q2whereC=total manufacturingcostperyearandQ=number of units produced per year.A newly hired employee, who previouslyworked for Bendix, tells Mr. Spade that Bendix isnow producing 110 units per year. If the selling priceremains unchanged,Sam wonders if Bendix is likelyto increase the number of units produced per year inthe near future. He asks you to look at the informationand tell him what you are able to deduce from it

A small company manufactures a certain product.Variable costs are $20 per unit and fixed costs are$10,875. The pricedemand relationship for thisproduct isP=0.25D+250, wherePis theunit sales price of the product andDis the annual demand. Use the data (and helpful hints) that followto work out answers to parts (a)(e).Total cost=Fixed cost+Variable costRevenue=DemandPriceProfit=RevenueTotal costSet up your graph with dollars on theyaxis (between0 and $70,000) and, on thexaxis, demandD: (unitsproduced or sold), between 0 and 1000 units.(a)Develop the equations for total cost and totalrevenue.(b)Find the breakeven quantity (in terms of profitand loss) for the product.(c)What profit would the company obtain bymaximizing its total revenue?(d)What is the companysmaximumpossible profit?(e)Neatly graph the solutions from parts(a),(b),(c),and(d).

A firm believes a products sales volume (S) dependson its unit selling price (P)asS=$100P.Theproduction cost (C) is $1000+10S.(a)Draw a graph with the sales volume (S) from 0 to100 on thexaxis, and total cost and total incomefrom $0 to $2500 on theyaxis. On the graphdraw the lineC=$1000+10S. Then plot thecurve of total income. Mark the breakeven pointson the graph.(b)Determine the breakeven point (lowest sales vol-ume at which total sales income just equals totalproduction cost). (Hint:This may be done bytrial and error or by using the quadratic equationto locate the point at which profit is zero.)(c)Determine the sales volume (S)atwhichthefirms profit is a maximum. (Hint:Write anequation for profit and solve it by trial and error,or as a minimamaxima calculus problem.)

A labor-intensive processhas a fixed costof $338,000and a variable cost of $143 per unit. A capital- intensive (automated) process for the same producthas a fixed cost of $1,244,000 and a variable cost of$92.50 per unit. How many units must be producedand sold at $197 each for the automated process tobe preferred to the labor-intensive process.Contributedby PaulR. McCright,Universityof SouthFlorida

Heinrich is a manufacturing engineer with the MillerCompany. He has determined the costs of producinga new product to be as follows Equipment cost: $288,000/yearEquipment salvage value at EOY5 = $41,000Variable cost per unit of production: $14.55Overhead cost per year: $48,300If the Miller Company uses a 5-year planning horizonand the product can be sold for a unit price of $39.75,how many units must be produced and sold each yearto break even?Contributed by Paul R. McCright, University ofSouth Florida

An assembly line can produce 90 units per hour. Thelines hourly cost is $4500 on straight time (the first8 hours). Workers are guaranteed a minimum of 6hours. There is a 50% premium for overtime, how-ever, productivity for overtime drops by 5%. Whatare the average and marginal costs per unit for thefollowing daily quantities?(a)450(b)600(c)720(d)900

A pump has failed in a facility that will be completelyreplaced in 3 years. A brass pump costing $6000installed will last 3 years. However, a used stainlesssteel pump that should last 3 more years has been sit-ting in the maintenance shop for a year. The pumpcost $13,000 new. The accountants say the pump isworth $7000 now. The maintenance supervisor saysthat it will costan extra $500 to reconfigure the pumpfor the new use and that he could sell it used (as is)for $4000.(a)What is the book cost of the stainless steel pump?(b)What is the opportunity cost of the stainless steelpump?(c)How much cheaper or more expensive would itbe to use the stainless steel pump rather than anew brass pump?

Last year to help with your New Years resolutionsyou purchased a $500 piece of fitness equipment.However, you use it only once a week on average.It is December, and you can sell the equipment for$200 (to someone with a New Years resolution)and rely on the university gym until you graduate inMay. If you dont sell until May, you will get only$100. If you keep the heavy piece, youll have to pay$25 to move it to the city of your new job (whereyou interned last summer). There is no convenient gym at the new location. What costs and intangibleconsequences are relevant to your decision? Whatshould you do?

Bob Johnsondecided to buy a new home. After look-ing at tracts of new homes, he decided that a custom-built home was preferable. He hired an architect toprepare the drawings. In due time, the architect com-pleted the drawings and submitted them. Bob likedthe plans; he was less pleased that he had to pay thearchitect a fee of $7000 to design the house. Bobasked a building contractor to provide a bid to con-struct the home on a lot Bob already owned. Whilethe contractor was working to assemble the bid, Bobcame across a book of standard house plans. In thebook was a home that he and his wife liked betterthan the one designed for them by the architect. Bobpaid $200 and obtained a complete set of plans forthis otherhouse.Bob then askedthe contractorto pro-vide a bid to construct this stock plan home. In thisway Bob felt he could compare the costs and makea decision. The building contractor submitted thefollowing bids:Custom-designed home $258,000Stock-plan home 261,000Bob was willing to pay the extra$3000 for it. Bobswife, however, felt they should go ahead with thecustom-designed home, for, as she put it, We cantafford to throw away a set of plans that cost $7000.Bob agreed, but he disliked the thought of building ahome that is less desirable than the stock plan home.Then he asked your advice. Which house would youadvise him to build? Explain

You are reevaluating the pump choice that was madelast year by your boss. The expected cost savingshave not occurred because the pump is too small.ChoiceA, at $90,000, is to replace the pump withone that is the right size and sell the old one. ChoiceB, at $100,000, is to buy a small pump to use in tan-dem with the existing pump. The two-pump solutionhas slightly higher maintenance costs, but it is moreflexible and reliable. What criteria should you use?Which choice would you recommend, and why?

Consider the situation of owning rental propertiesthat local university students rent from you for theacademic year. Develop a set of costs that you couldclassify as recurring and others that could be classi-fied as nonrecurring.

List and classify your costs in this academic year asrecurring or nonrecurring

Define the difference between a cash cost and abook cost. Is engineering economic analysis con- cerned with both types of cost? Give an exampleof each, and provide the context in which it isimportant.

In your own words, develop a statement of what theauthors mean by life-cycle costs. It is important fora firm to be aware of life-cycle costs. Can you explainwhy?

Most engineering students own a computer. Whatcosts have you incurred at each stage of your com- puters life cycle? Estimate the total cost of owner-ship. Estimate the benefits of ownership. Has it beenworth it?

Estimating benefits is often more difficult than costestimation. Use the example of car ownership todescribe the complicating factors in estimating thecosts and benefits.

In looking at Figures 2-4 and 2-5, restate in your ownwords what the authors are trying to get across withthese graphs. Do you agree that this is an importanteffect for companies? Explain.

In the text we describe three effects that compli-cate the process of making estimates to be usedin engineering economy analyses. List these threeeffects and comment on which might be the mostinfluential.

Develop an estimate for each of the followingsituations.(a)The cost of a 500-mile automobile trip, if gaso-line is $3 per gallon, vehicle wear and tear is$0.50 per mile, and our vehicle gets 20 miles pergallon.(b)The total number of hours in the average humanlife, if the average life is 75 years.(c)The number of days it takes to travel around theequator using a hot air balloon, if the balloonaverages 100 miles per day, the diameter of theearth is4000 miles.(d)The total area in square miles of the UnitedStates of America, if Kansas is an average-sizedstate. Kansas has an area of 390 miles200miles.

Northern Tundra Telephone (NTT) has received acontract to install emergency phones along a new 100-mile section of the Snow-Moose Turnpike. Fiftyemergency phone systems will be installed about2 miles apart. The material cost of a unit is $125.NTT will need to run underground communicationlines that cost NTT $7500 per mile (including labor)to install. There will also be a one-time cost of$10,000 to network these phones into NTTs currentcommunication system.(a)Develop a cost estimate of the project fromNTTs perspective.(b)If NTT adds a profit margin of 35% to its costs,how much will it cost the state to fund theproject?

You and your spouse are planning a second honey-moon to the Cayman Islands this summer and wouldlike to have your house painted while you are away.Estimate the total cost of the paint job from theinformation given below, where:Costtotal=Costpaint+Costlabor+CostfixedPaint information:Your house has a surface areaof 6000 ft2. One can of paint can cover 300 ft2.You are estimating the cost to put ontwo coatsofpaint for the entire house.Number of CansPurchased Cost per CanFirst 10 cans purchased $15.00Second 15 cans purchased $10.00Up to next 50 cans purchased $7.50Laborinformation:You plan to hire five painterswho will paint for 10 hours per day each. Youestimate that the job will require 4.5 days of theirpainting time. The painters rate is $8.75 per hour.Fixed cost information:The painting com-pany charges $1200 per job to cover travelexpenses, clothing, cloths, thinner, administra-tion, and so on

You want a mountain cabin built for weekend trips,vacations, to host family, and perhaps eventually toretire in. After discussing the project with a localcontractor, you receive an estimate that the totalconstruction cost of your 2000-ft2lodge will be$250,000. The percentage of costs is broken down asfollows: Cost ItemsTotal CostsConstruction permits, legal and8title feesRoadway, site clearing, preparation 15Foundation, concrete, masonry 13Wallboard, flooring, carpentry12Heating, ventilation, air13conditioning (HVAC)Electric, plumbing, communications 10Roofing, flooring12Painting, finishing17100(a)What is the cost per square foot of the 2000-ft2lodge?(b)If you are also considering a 4000-ft2layoutoption, estimate your construction costs if:i.All cost items (in the table) change propor-tionately to the size increase.ii.The first two cost items do not change at all;HVAC changes by 50%; and all others areproportionate

SungSam, Inc. is designing a new digital camcorderthat is projected to have the following per-unit coststo manufacture:Cost Categories Unit CostsMaterials costs $ 63Labor costs24Overhead costs 110Total unit cost$197SungSam adds 30% to its manufacturing cost forcorporate profit.(a)What unit profit would SungSam realize on eachcamcorder?(b)What is the overall cost to produce a batch of10,000 camcorders?(c)What would SungSams profit be on the batch of10,000 if historical data show that 1% of prod-uct will be scrapped in manufacturing, 3% offinished product will go unsold, and 2% ofsoldproduct will be returned for refund?(d)How much can SungSam afford to pay for a con-tract that would lock in a 50% reduction in theunit material cost previously given? If SungSamdoes sign the contract, the sales price will notchange.

Estimate the cost of expanding a planned new clinicby 20,000 ft2. The appropriate capacity exponent is0.66, and the budgetestimate for 200,000 ft2was $15million. (Answer: $1 million

Fifty years ago, Grandma Bell purchased a setof gold-plated dinnerware for $55, and last yearyou inherited it. Unfortunately a fire at your homedestroyedthe set. Your insurance companyis at a lossto define the replacement cost and has asked yourhelp. You do some research and find that the AurumFlatware Cost Index (AFCI) for gold-plated dinner-ware, which was 112 when Grandma Bell bought herset, is at 2050 today. Use the AFCI to update the costof Bells set to todays cost to show to the insurancecompany.

Your boss is the director of reporting for the AthensCounty Construction Agency (ACCA). It has beenhis job to track the cost of construction in AthensCounty. Twenty-five years ago he created the ACCACost Index to track these costs. Costs during the firstyear of the index were $12 per square foot of con-structed space (the index value was set at 100 forthat first year). This past year a survey of contractorsrevealed that costs were $72 per square foot. Whatindex number will your boss publish in his report forthis year? If the index value was 525 last year, whatwas the cost per square foot last year?

A new aerated sewage lagoon is required in a smalltown. Earlier this year one was built on a similarsite in an adjacent city for $2.3 million. The newlagoon will be 60% larger. Use the data in Table 2-1to estimate the cost of the new lagoon

A refinisher of antiques named Constance has beenso successfulwith her small business that she is plan-ning to expand her shop. She is going to start enlarg-ing her shop by purchasing the following equipment.Cost of Power- NewOriginal Original Sizing EquipmentEquipment Size Equipment Exponent SizeVarnish bath 50 gal $3500 0.80 75 galPower scraper 3/4 hp $250 0.22 1.5 hpPaint booth 3 ft3$3000 0.6 12 ft3What wouldbe thenetcostto Constanceto obtain thisequipmentassume that she can trade the old equip-ment in for 15% of its original cost. Assume there hasbeen no inflation in equipment prices.

Refer to Problem 2-41 and now assume the pricesfor the equipment that Constance wants to replacehave not been constant. Use the cost index data foreach piece of equipment to update the costs to theprice that would be paid today. Develop the overallcost for Constance, again assuming the 15% trade-in allowance for the old equipment. Trade-in value isbased on original cost.

Five years ago, when the relevant costindex was 120,a nuclear centrifuge cost $40,000. The centrifugehad a capacity of separating 1500 gallons of ionizedsolution per hour. Today, it is desired to build a cen-trifuge with capacity of 4500 gallons per hour, butthe cost index now is 300. Assuming a power-sizingexponent to reflect economies of scale,x, of 0.75,use the power-sizing model to determine the approx-imate cost (expressed in todays dollars) of the newreactor.

Padre works for a trade magazine that publisheslists of power-sizing exponents (PSE) that reflecteconomies of scale for developing engineering esti-mates of various types of equipment. Padre has beenunable to find any published data on the VMICmachine and wants to list itsPSEvalue in his nextissue. Given the following data (your staff was ableto find data regarding costs and sizes of the VMICmachine) calculate thePSEvalue that Padre shouldpublish. (Note:The VMIC-100 can handle twice thevolume of a VMIC-50.)Cost of VMIC-100 today $100,000Cost of VMIC-50 5 years ago $45,000VMIC equipment index today=214VMIC equipment index 5 years ago=151

Determine the time required to produce the 2000thitem if the first item requires 180 minutes to produceand the learning-curve percentage is 92%. (Answer:72.1 minutes

If 200 labor hours were required to produce the1stunit in a production run and 60 labor hours were required to produce the 7thunit, what was thelearning-curve rateduring production?

Rose is a project manager at the civil engineer-ing consulting firm of Sands, Gravel, Concrete, andWaters, Inc. She has been collecting data on a projectin which concrete pillars were being constructed;however not all the data are available. She has beenable to find out that the 10thpillar required 260person-hours to construct, and that a 75% learningcurve applied. She is interested in calculating thetime required to construct the 1stand 20thpillars.Compute the values for her.

Sally Statistics is implementing a system of statisti-cal process control (SPC) charts in her factory in aneffort to reduce the overall cost of scrapped product.The current cost of scrap is $Xper month. If an 80%learning curve is expectedin the use of the SPC chartsto reduce the cost of scrap, what would thepercent-agereductionin monthly scrapcostbe after the chartshave been used for 12 months? (Hint:Model eachmonth as a unit of production.)

Randy Duckout has been asked to develop an esti-mate of theper-unit selling price(the price that eachunit will be sold for) of a new line of handcraftedbooklets that offer excuses for missed appoint- ments. His assistant Doc Duckout has collectedinformation that Randy will need in developing hisestimate:Cost of direct labor $20 per hourCost of materials$43.75 per batchof 25 bookletsCost of overhead items 50% of direct laborcostDesired profit20% of totalmanufacturing costDoc also finds out that (1) they should use a 75%learning curve for estimating the cost of direct labor,(2) the time to complete the 1stbooklet is estimatedat 0.60 hour, and (3) the estimated time to completethe 25thbooklet should be used as their standard timefor the purpose of determining theunit selling price.What would Randy and Docs estimate be for theunitselling price?

Develop a statement that expresses the extent towhich cost-estimating topics also apply to estimatingbenefits. Provide examples to illustrate.

Large projects, such as a new tunnel under the Hud-son, the Big Dig in Boston, the Denver airport, a newmilitary jet, and a natural gas pipeline from Alaska tothe Midwest, often take 5 to 15 years from concepttocompletion.(a)Should benefit and cost estimates be adjusted forthe greater influences and impacts of inflation,government regulatory changes, and changinglocal economic environments?Why or why not?.(b)How does the public budget-making processinteract with the goal of accurate benefit and costestimating for these large projects?Contributed by Morgan Henrie, University of AlaskaAnchorage

On December 1, Al Smith purchased a car for$18,500. He paid $5000 immediately and agreed topay three additional payments of $6000 each (whichincludes principal and interest) at the end of 1, 2, and3 years.Maintenance for the car is projected at $1000atthe endof the first yearand $2000atthe end of eachsubsequent year. Al expects to sell the car at the endof the fourth year (after paying for the maintenancework) for $7000. Using these facts, prepare a table ofcash flows.

Bonka Toys is considering a robot that will cost$20,000 to buy. After 7 years its salvage value will be $2000. An overhaul costing $5000 will be neededin Year 4. O&M costs will be $2500 per year. Drawthe cash flow diagram

Pine Village needs some additional recreation fields.Construction will cost $225,000, and annual O&Mexpenses are $85,000. The city council estimates thatthe value of added youth leagues is about $190,000annually. In year 6 another $75,000 will be neededto refurbish the fields. The salvage value is estimatedto be $100,000 after 10 years. Draw the cash flowdiagram.

Identify your major cash flows for the current schoolterm as first costs, O&M expenses, salvage values,revenues, overhauls, and so on. Using a week as thetime period, draw the cash flow diagram.