# Answer to Question #75992 in Microeconomics for Neizer

Question #75992

A firm produces two products, milk and cheese Q1 and Q2 represent the output rates for milk and cheese, respectively. The profit function is Ï€= -50 + 10Q1 + 20Q2 - Q1'2 - 2Q2'2 - 2Q1Q2

Determine the output rate for each product that will maximise profit

Determine the output rate for each product that will maximise profit

Expert's answer

The profit function is Ï€ = -50 + 10Q1 + 20Q2 - Q12 - 2Q22 - 2Q1Q2 â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦..(1)

Now, to determine the rate of output for each product that will maximize profit we need to find derivative from the profit function , which is equals to zero.

Taking derivative of equation (1) with respect to Q1 ,keeping Q2 constant we get,

dÏ€/dQ_1 =10-2Q_1-2Q_2 = 0

Or, Q_1+Q_2= 5 â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦(2)

Taking derivative of equation (1) with respect to Q2 ,keeping Q1 constant we get,

dÏ€/dQ_2 =20-4Q_2-2Q_1 = 0

Or, Q_1+ã€–2Qã€—_2 =10 â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦..(3)

Solving equation (2) and (3) we get, Q1 = 0 and Q2 = 5.

Now, to determine the rate of output for each product that will maximize profit we need to find derivative from the profit function , which is equals to zero.

Taking derivative of equation (1) with respect to Q1 ,keeping Q2 constant we get,

dÏ€/dQ_1 =10-2Q_1-2Q_2 = 0

Or, Q_1+Q_2= 5 â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦(2)

Taking derivative of equation (1) with respect to Q2 ,keeping Q1 constant we get,

dÏ€/dQ_2 =20-4Q_2-2Q_1 = 0

Or, Q_1+ã€–2Qã€—_2 =10 â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦â€¦..(3)

Solving equation (2) and (3) we get, Q1 = 0 and Q2 = 5.

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