A company manufactures two products. The price function for product A is p = 20

Question

A company manufactures two products. The price function for product A is p = 20 - 1/2x (for 0 lessthanorequalto x lessthanorequalto 40), and for product B is q = 34 - y (for 0 lessthanorequalto y lessthanorequalto 34), both in thousands of dollars, where x and y are the amounts of products A and B, respectively, If the cost function is C(x, y) = 10x + 20y - xy + 14 thousands of dollars, find the quantities and the prices of the two products that maximize profit. product A quantity units product A price thousand dollars product B quantity units product B price thousand dollars Find the maximum profit. thousand dollars

Explanation / Answer

Ans)

p = 20 - (1/2)x

At x = 0 , p = 20

At x = 40 , p = 0

diff in p = 20

Product A quantity is 20 units

Product A price is 20 thousand dollars

for product B,

q = 34 - y

At y = 0, q = 34

At y = 34, q = 0

diff in q = 34

Product B quantity is 34 units

Product B price is 34 thousand dollars

c(x,y) = 10x + 20y - xy +14

for x= 20 and y = 34, we get

c(20,34) = 200 + 680 - 680 + 14 = 214

max profit is 214 thousand dollars

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