Solve the linear programming problem.
-A candy company has 135 pounds of cashews and 180 pounds of peanuts which they combine into twodifferent mixes. The deluxe mix has half cashews and half peanuts and sells for $6 per pound. Theeconomy mix has one third cashews and two thirds peanuts and sells for $5.90 per pound. How manypounds of each mix should be prepared for maximum revenue?
A)180 deluxe, 135 economy
B)270 deluxe, 90 economy
C)90 deluxe, 45 economy
D)135 deluxe, 0 economy

Question

Quizplus · Accepted Answer

The correct answer is A.The deluxe mix has half cashews and half peanuts, so it uses 67.5 pounds of cashews and 67.5 pounds of peanuts. The economy mix has one third cashews and two thirds peanuts, so it uses 45 pounds of cashews and 90 pounds of peanuts.The deluxe mix sells for $6 per pound, so the revenue from selling x pounds of deluxe mix is 6x. The economy mix sells for $5.90 per pound, so the revenue from selling y pounds of economy mix is 5.90y.The total revenue from selling x pounds of deluxe mix and y pounds of economy mix is 6x + 5.90y.We want to maximize the total revenue, subject to the constraints that we have 135 pounds of cashews and 180 pounds of peanuts.The constraints are:x + y <= 135 (cashews)x + y <= 180 (peanuts)We can graph these constraints to find the feasible region. The feasible region is the shaded area in the graph below.[Image of a graph with two lines intersecting at (135, 0) and (0, 180). The shaded area is the feasible region.]The maximum value of the total revenue occurs at the corner point of the feasible region that is furthest from the origin. This corner point is (180, 135).Therefore, the candy company should prepare 180 pounds of deluxe mix and 135 pounds of economy mix for maximum revenue.

Solve the Linear Programming Problem