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Indiana Petroleum Company’s Profit is a function of Q1 = heating oil and Q2 = gasoline:...

Indiana Petroleum Company’s Profit is a function of Q1 = heating oil and Q2 = gasoline: Π = -50 +120*Q1 + 90*Q2 – 9*Q12 – 8*Q22 – 2*Q1*Q2. Find the profit-maximizing amounts of Q1 and Q2 as well as the profit. You can use excel.

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Answer #1

the objective function is given by:

-50 +120*Q1 + 90*Q2 – 9*Q12 – 8*Q22 – 2*Q1*Q2

Taking FOC wrt Q1 and Q2 and equation to 0 we get:

Q1: 120 - 18Q1 - 2Q2 = 0 => 18Q1 + 2Q2 = 120 ........................(1)

Q2: 90 - 16Q2 - 2Q1 = 0 => 16Q2 + 2Q1 = 90............................(2)

8*(1) - (2)

=> 144Q1 + 16Q2 - 16Q2 - 2Q1 = 870

=> 142Q1 = 870

=> Q1 = 870/142 = 6.12

=> Q2 = (120 - 18* 870/142 -)/2 = 1380 / 284 = 4.85

Maximum profits = -50 +120*(870/142) + 90*(1380 / 284) - 9(870/142)2 - 8(1380 / 284)2 - 2*(870/142)*(1380 / 284)

= 536.26

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