mat 117 appendix C (brand new)
mat 117 appendix C (brand new)
CSU - Dominguez hills
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Date Created: 11/16/15
Axia College Material Appendix C Polynomials Retail companies need to keep close track of their operations in order to maintain profitability Often the sales data of each individual product is analyzed separately which can be used to help set pricing and other sales strategies Application Practice Answer the following questions Use Equation Editor to write mathematical expressions and equations First save this file to your hard drive by selecting Save As from the File menu Click the white space below each question to maintain proper formatting 1 In this problem we will analyze the profit found for sales of decorative tiles A demand equation sometimes called a demand curve shows how much money people would pay for a product depending on how much of that product is available on the open market Often the demand equation is found empirically through experiment or market research a Suppose that a market research company finds that at a price of p 20 they would sell x 42 tiles each month If they lower the price to p 10 then more people would purchase the tile and they can expect to sell x 52 tiles in a month s time Find the equation of the line for the demand equation Write your answer in the form p mx b Hint Write an equation using two points in the form xp pmxb Putting the values E the equation Two points are 4220 5210 20m42b 1 10m52b 2 20m42b 10m52b Adding them 2042mb 10 52m b 10 10m m 1 MAT 117 hence m 1 put the value of mE equation 2 Z get the value of b 10m52b 10 152b 10 52b 1052b 6219 therefore the equation is p x62 A company s revenue is the amount of money that comes in from sales before business costs are subtracted For a single product you can find the revenue by multiplying the quantity of the product sold x by the demand equation p b Substitute the result you found from part a into the equation R xp to find the H H2 EEH revenue equation Provide your answer in simplified form The costs of doing business for a company can be found by adding fixed costs such as rent insurance and wages and variable costs which are the costs to purchase the product you are selling The portion of the company s fixed costs allotted to this product is 300 and the supplier s cost for a set of tile is 6 each Let x represent the number of tile sets c If b represents a fixed cost what value would represent b b300zcost d find the cost equation for the tile Write your answer in the form C mx b variable cost Vadditional cost per tile m 6 variable costs therefore cost equation for x tiles is given as C x 6 x 300 Cost is E dollars The profit made from the sale of tiles is found by subtracting the costs from the revenue 9 Find the Profit Equation by substituting your equations for R and C in the equation P R C Simplify the equation ProfitRevenue Costs Revenue x2 62x Cost 6x300 Therefore profitP P x262x 6x300 P x262x 6 x 300 P x 256 x 300 MAT 117 Pro t is E dollars What is the profit made from selling 20 tile sets per month Putting x 20 we get profit as P x256x 300 P 2025620 300 P 4001120 300 P 420 What is the profit made from selling 25 tile sets each month Putting x225 we get pro t as P x256x 300 P 2525625 300 P 625 1400 300 P475 What is the profit made from selling no tile sets each month Interpret your answer Putting x 0 we get P x 256 36 300 P 02560 300 P 0 0 300 P 300 Therefore company will be E loss this cost is actually the 3 cost Use trial and error to find the quantity of tile sets per month that yields the highest profit For a quadratic equation with a negative leading coefficient there is always a maximum value at the vertex which is located on the equation39s Axis of Symmetry x25p475 x26p480 x27p483 x28p484 x29p483 x30p480 Vertex of the equation is given as X b 2a 56 x 28 2 y x256x 300 y 2825628 300 MAT 117 y 7841568 300 y484 xy28484 j How much profit would you earn from the number you found in part i P x256x 300 P 28256 28 300 P 7841568 300 P 484 Therefore maximum pro t 2 484 k What price would you sell the tile sets at to realize this profit hint use the demand equation from part a Price for the tile is given as P x 62 P 28 62 Price per tile 2 34 2 The break even values for a profit model are the values for which you earn 0 in profit Use the equation you created in question one to solve P 0 and find your break even values PuttingPZ 0 x256x 3000 x2 56x3000 x2 50x 6x3000 x 50x 60 x 50V x6 The company will break even if they sell 50 sets or 3 sets of tiles 3 In 2002 Home Depot s sales amounted to 58200000000 In 2006 its sales were 90800000000 a Write Home Depot s 2002 sales and 2006 sales in scientific notation 2002 582 gtlt1010 2006 908 gtlt1010 You can find the percent of growth in Home Depot s sales from 2002 to 2006 follow these steps 0 Find the increase in sales from 2002 to 2006 MAT 117 c Find what percent that increase is of the 2002 sales b What was the percent growth in Home Depot s sales from 2002 to 2006 Do all your work by using scientific notation IncreaseEhome sales 2 Z 908 x 1010 582x 1010 2326 gtlt1010 Percent increase would be the increase divided by the starting point 2002 X Z 326 x 1010 582 x 1010 5601 increase V about a 56 increase x1005601 source Home Depot Annual Report for FY 2006 httpwww6homedepotcomannualreportindexhtmI 4 A customer wants to make a teepee in his backyard for his children He plans to use lengths of PVC plumbing pipe for the supports on the teepee and he wants the teepee to be 12 feet across and 8 feet tall see figure How long should the pieces of PVC plumbing pipe be W How long is the PVC pipe 12 feet MAT 117 2 2 2 61 26 122 82262 2 6282262 c6282 c100 c10feet MAT 117
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