Rnd the value of the objective function z - 2x + 3y at each comer of lhe graphed region

In Exercises 1-5, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. v - 4x + J 1r + 2y - 13

In Exercises 1-5, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. { X+ 4y - 14 2r - y - 1

In Exercises 1-5, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. S.t + 3y - 1 3x + 4y - - 6

In Exercises 1-5, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. 2v - 6x - 7 . 3x - y - 9

In Exercises 1-5, solve by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets. 4x - 8v - 16 3x - 6y - 12

A company is planning lo manufaclure computer desks. 7. The fixed cost will be $60,000 and it 11ill cost $200 to produce each desk. Each desk will be sold lor $450. a. Write the cost unction,~ of producing x desks. b. Write the revenue runc.tion, R, from thesaJe of xdesks. c. Detem1inc the break-even point Describe what this means

Talk about painting'i by numbers: In 2007, lhis glitte1ing Klimt set the record for the most ever paid for a painting, a title that had been held by Picasso's Boy with a Pipe. Combined. the two paintings sold for $?..39 million. The difference between the selling price for Klimt's work and the selling price lor Picasso's \vork was $31 million. Find the amount paid ror each painting

The music business is evol, ng into a digital marketplace. 1lle bar graph shows Uta! from 2004through 2009, CD album sales declined, while digital track sales grew. 1400 1200 1000 800 600 400 200 SOUIC" Rl AA Sales of Albums and Digital Traru in the United States Digital track sales CD albwn sales 770 142 2001 868 Sit 2fJJI Year 1237 293 2009 a. In 2004, 142 million digital tracks were sold. For the period shown by the graph. this has increased at 311 average rate of 219 million digital tracks per year. Write a function that models the sale of digitaltracks, y, in millions,x years after2004. b. llte function 95x + y - 770 models the number of albums sold, Y~ in millions, x years after 2004. Use lhis model and the model you obtained in part (a) to detemtine when digital trac.k sales caught up with album sales. How many digital tracks and how many albums were sold in thal year?

The perimeter of o rectangular t"blc top is34 fcct.'ll>c difference between 4 times the length "nd 3timcs the "idth is 33 feet. Find the dimensions.

A travel agent offers two p:w:kage vacation plans. The first plan costs $360 and includes 3 da)~ at hotel ond a rental cor for 2 day!. The second pion costs SSOO and includes~ da~ at a hotel and a rental car for 3 days. The daily chorgc for the hotel is the same under each plan, as is the daily charge for the car. Find tile rost per day for the hotel and for the car.

The caloric-nutrient information for on apple and an a>-ocado is g;,..,n in the table. How many of each should be eaten to get eXliCIJy tOOl calories and 100 grams of carbohydrates? Calories Carbohydrates (gmms)

Solve each system in Exercises 12-13. lt - y + : - 1 3x - 3y + 4: - 5 4x - 2y + 3: - 4

Solve each system in Exercises 12-13. X + 2y - : - 5 2< - y + 3: - 0 2y + : - 1

Find the quadratic funclion y - a.\'2 + bx + c whose graph passes through the points (1,4). (3,20).nnd (-2, 25).

20th Century n Death 11te gi'CiltO.<I c:ouse of denlll in lhc 20th century was disease. killing 1390 million people. 'lho bar graph shows the five leading c:nu$C:S of dc.nth in Chal ocnlury. excluding disease. Number ol O.oths in the 20th Cnhary, by Cause < 10 War F.lmin< Toboc<o Swride Murder Cause ol Oelh Soorre: \\lkipedia War, famine. and tobacco c:ombi.W result'<l in 306 million death!. The difference between the number of deaths from war and famine was 13 million. "lbc difference bet\\ecn the number of deaths from war and tobocw w"" 53 million. Find the number or 20th century deaths from w~r. !amine. and tobacro.

In Exercises 16-24, write the partial decomposition of each rational expression. x ' (x 3)(x + 2)

In Exercises 16-24, write the partial decomposition of each rational expression. llx - 2 x' - ,r - 12

In Exercises 16-24, write the partial decomposition of each rational expression. 4x2 - 3x - 4 t -;::.--,,;:;:..----''"' x(x ~ 2)(x 1)

In Exercises 16-24, write the partial decomposition of each rational expression. 2x - I ' (X - 2)

In Exercises 16-24, write the partial decomposition of each rational expression. 2x - 6 (x - 1)(x - 2)-

In Exercises 16-24, write the partial decomposition of each rational expression. 3x ' (x - 2)(r+ I)

In Exercises 16-24, write the partial decomposition of each rational expression. c.7=.x'_-_.:7=.x"'Tc...=23:.. (x - 3)(.r' + )

In Exercises 16-24, write the partial decomposition of each rational expression. x' ----'"---. (x' + ~)'

In Exercises 16-24, write the partial decomposition of each rational expression. 4.,.; + it' + 7x - 1 .=:........:...:o:..._.:....:..::....,-.:. (x1 - x - 1)'

In Exercises 25-35, solve each system by the method of your choice. {sy -.r - , 26 {,. - .r> T 2x .,.. , x - y - 1

In Exercises 25-35, solve each system by the method of your choice. {,. - .r> T 2x .,.. , x - y - 1 x+y - 1

In Exercises 25-35, solve each system by the method of your choice. x' - r' - 2 X + y - 0

In Exercises 25-35, solve each system by the method of your choice. {2r> - y> - ~ . ' , X + y - 0 .r - y- IS

In Exercises 25-35, solve each system by the method of your choice. {'ry -4-0 y - x - 0

In Exercises 25-35, solve each system by the method of your choice. {v 1 --lx X - 2y + 3 - 0

In Exercises 25-35, solve each system by the method of your choice. {''' + y' - 10 y - x+2

In Exercises 25-35, solve each system by the method of your choice. XV -I y - 2<+1

In Exercises 25-35, solve each system by the method of your choice. {'t+y+ J - 0 x 2 + y2 + 6y - x - - 5

In Exercises 25-35, solve each system by the method of your choice. {''' ~ y' - 13 x'- y - 7

In Exercises 25-35, solve each system by the method of your choice. {2x' + 3/ - 21 3x2 - 4y2 - 23

The perimeter of a rectangle is 26 meters and its area is 40 $quare meters. Find its dimensions.

Find lhe coordinates of all points (x, y) that lio on tho line whose equation is 2t + y - 8, so that the area of the rectangle shown in the figure is 6 square units. )'

Two adjoining square fields "ith on area of 2900 square feet arc to he endooed "ith 2.j() feet of fencing. The situation is represented in the figure. Find the length ol each side where n ,ariable appears.

In Exercises 39-45, graph each inequality. 3x - 4y > 12

In Exercises 39-45, graph each inequality. y s: - 2x + 2

In Exercises 39-45, graph each inequality. X< - 2

In Exercises 39-45, graph each inequality. y :. 3

In Exercises 39-45, graph each inequality. x2 + y2 > 4

In Exercises 39-45, graph each inequality. y s: x2 - J

In Exercises 39-45, graph each inequality. y s: 2'

In Exercises 46-55, graph the solution set of each system of inetJualities or indicate that the system has no solution. 47. { 3x + 2y ,. 6 2r+ y :a: 6

In Exercises 46-55, graph the solution set of each system of inetJualities or indicate that the system has no solution. 2x - y ,. 4 2 x+2y < 2

In Exercises 46-55, graph the solution set of each system of inetJualities or indicate that the system has no solution. )' <X y s: 2

In Exercises 46-55, graph the solution set of each system of inetJualities or indicate that the system has no solution. {X + V S 6 y 2 2t - 3

In Exercises 46-55, graph the solution set of each system of inetJualities or indicate that the system has no solution. {Os:xs: 3 y > 2

In Exercises 46-55, graph the solution set of each system of inetJualities or indicate that the system has no solution. {2r + y < 4 2r + y > 6

In Exercises 46-55, graph the solution set of each system of inetJualities or indicate that the system has no solution. {x' + y' s: 16 x+y < 2

In Exercises 46-55, graph the solution set of each system of inetJualities or indicate that the system has no solution. {x' +y' s: 9 y < - 3x +I

In Exercises 46-55, graph the solution set of each system of inetJualities or indicate that the system has no solution. r x + y < 6 3x + 2y :. y < x+6

In Exercises 46-55, graph the solution set of each system of inetJualities or indicate that the system has no solution. y 0 3x + 2y :. 4 x - y s: 3

Rnd the value of the objective function z - 2x + 3y at each comer of lhe graphed region shown. What is the maximum value of lhe objective function? What is the minimum value of the objeclive function? y In Exercises 57-59, graph the region determined by the constraims. Then find the maximum value of the given objective function, subjeclto the constraiJJts.

In Exercises 57-59, graph the region determined by the constraims. Then find the maximum value of the given objective function, subjeclto the constraints. Objective Function Constraints z - 2t + 3y { X '". 0. )' 2 0 x+ y s: 8 1r + 2y :. 6

In Exercises 57-59, graph the region determined by the constraims. Then find the maximum value of the given objective function, subjeclto the constraiJJts. Objective Function Constraints Z - X + 4y { 0 s: X s: S,O s: y s: 7 x + y :. 3

In Exercises 57-59, graph the region determined by the constraims. Then find the maximum value of the given objective function, subjeclto the constraiJJts. Objective Function Constraints z - 5x + 6y l .r "' O,y "' 0 )' S: X 2x + y s: 12 2x + 3)' ,. 6

A paper manufacturing company converts wood pulp to writing pape.r and newsprint The profit on a unit of writing paper is $500 and the profit on a unit of newsprint is $350. a. Let x represent the number of units of writing paper produced daily. Let y represent the numbe r of units or newsprint produced dail)'. \Vrite the objective function that models total daily profit. b. 1l1e manufacturer is bound by the following constraints: Equipment in the factory allows for making at most 200 units of paper (writing paper and newsprint) in a day. Regular customers require at least 10 units of writing paper and at least SO units of newsprint daily. \Vrite a system of inequalities that models these constraints. c. GrJpb the inequalities in part (b). Useonlythe first quadrant, because x and y must both be positive. (Suggestion: Let each unit along thex- and y-axcs reprcsent 20.) d. Evaluate the objective function at each or the three vertices or the graphed region. e. Complete the missing portions of this statement: The company will make the greatest profit by produc.ing __ units of writing paper and __ units of newsprint each day. The maximum daily profit is$. __ _

A manufacturer of lightweight tents makes two models whose specifications are given in the following table: Model A ModelB Cutting 11me per Tent 0.9 hour 1.8 hours As.'it'mblv 11me per Tent 0.8 hour 1.2 hours On a monthly basis, the manufacturer has no more than 864 hours of labor available in the cutting department and at most 672 hours in the assembly division. The profits come to $25 per tent for model A and $40 per tent for model 8. How many of e.ach should be manufactured monthly to maximize the profit?