Answer to Question #75992 in Microeconomics for Neizer

Question

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

Determine the output rate for each product that will maximise profit

Answer 1

The profit function is π = -50 + 10Q1 + 20Q2 - Q12 - 2Q22 - 2Q1Q2 ……………………..(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,
dπ/dQ_1 =10-2Q_1-2Q_2 = 0
Or, Q_1+Q_2= 5 …………………………(2)
Taking derivative of equation (1) with respect to Q2 ,keeping Q1 constant we get,
dπ/dQ_2 =20-4Q_2-2Q_1 = 0
Or, Q_1+〖2Q〗_2 =10 ………………………..(3)
Solving equation (2) and (3) we get, Q1 = 0 and Q2 = 5.