Question #54147

A firm produces two products, milk and cheese, Q1 and Q2 represent the output rate for milk and cheese respectively. The profit function is

π = -100+20Q1+60Q2-10Q1^2-2Q1Q2

Determine the rate of output for each product that will maximize profit.

π = -100+20Q1+60Q2-10Q1^2-2Q1Q2

Determine the rate of output for each product that will maximize profit.

Expert's answer

To determine the rate of output for each product that will maximize profit we need to find derivative from the profit function - marginal profit MP, which should be equal zero MP = 0.

MP(Q1) = 20 - 20Q1 - 2Q2 = 0

MP(Q2) = 60 - 2Q1 = 0

Q1 = 30

20 - 600 - 2Q2 = 0

Q2 = -290

MP(Q1) = 20 - 20Q1 - 2Q2 = 0

MP(Q2) = 60 - 2Q1 = 0

Q1 = 30

20 - 600 - 2Q2 = 0

Q2 = -290

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## Comments

Assignment Expert21.08.15, 20:00Dear Asif, to maximize the profit function we need take derivatives on both variables (Q1 and Q2) and then solve obtained system of two equations simultaneously. In economics the derivation of profit with respect to the output means the Marginal Product (MP). Now we set two marginal products equal to zero and find the extremum. In fact, we have Q2=-290, and I guess your profit function has a mistake.

Asif20.08.15, 22:02Did not understand the answer of the above question Question #54147, please clarify it in easy way.

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