Question

1. You produce quesadillas (Q) with beef (B) and cheese (C). The production process is as so: Q = 40B – 1.5B^2 + 50C – 1.5C^2 Q=40B–1.5B 2 +50C–1.5C 2 The price of beef is $4 per box, and the price of cheese is $5 per box. The boxes are the same size and you only have room for 9 boxes in your freezer. How many boxes of cheese should be purchased?

Answer 1

Given production function, Q = 40B – 1.5B^2 + 50C – 1.5C^2

Price of beef = $4 per box

Price of cheese= $5 per box

At the profit-maximizing level, marginal products per dollar spent on each input should be equal

(Marginal product of beef/ Price of beef) = (Marginal product of cheese/Price of cheese)

It can be written as,

(Marginal product of beef/Marginal product of cheese) = ( Price of beef/Price of cheese)     ......(1)

MP of beef = dQ/dB = 40-3B

MP of cheese= dQ/dC= 50-3C

Substituting the value of MP into equation 1

(40-3B)/(50-3C) = 4/5

5(40-3B) = 4(50-3C)

-15B = - 12C

B = (4/5)C

It is given that total number of boxes should be 9

That is, B+C = 9

           (4/5)C +C = 9

           (9/5)C = 9

Therefore, C = 5

5 boxes of cheese should be purchased.