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The Kappa Beta fraternity has 200 sweatshirts and 100 pairs of sweatpants available to sell. During rush week, they decided to offer two package deals to students. Package A has one sweatshirt and one pair of sweatpants for $30. Package B has three sweatshirts and one pair of sweatpants for $50. The fraternity wants to sell at least 20 of Package A and at least 10 of Package B. How many of each package type must they sell in order to maximize their revenue?

Respuesta :

amna04352

Answer:

50 A and 50 B

Step-by-step explanation:

A》20

B》10

A + B》100 (for pants)

A + 3B》200 (for shirts)

A = 20

A + 3B = 200

3B = 180

B = 60

(20,60)

B = 10

A + B = 100

A = 90

(90,10)

A + B = 100

A = 100 - B

A + 3B = 200

100 - B + 3B = 200

2B = 100

B = 50

A = 100 - 50 = 50

(50,50)

Revenue:

30A + 50B

(20,10): 30(20) + 50(20)

= 1,100

(20, 60): 30(20) + 50(60)

= 3,600

(90,10): 30(90) + 50(10)

= 3,200

(50,50): 30(50) + 50(50)

= 4,000

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