Please any help????
A firm produces good A and good B, and faces demand functions for these two goods:
qA = 1000 * (20 − pA)
qB = 1000 * (20 − pB)
Its total cost function is: TC (qA, qB) = 4(qA + qB)+ (qA+qB)^{2}/4000
What are the profit-maximising quantities of the two goods to make and sell?
ANSWER: qA = qB = 5333.33. this is the answers but I want to know how the answer was obtained.
with many thanks.
Total profit is total revenue minus total cost. Revenue is units demanded times price per unit. Hence we have:
Total revenue:
and so the total profit is:
Next, find the partial derivatives and equate to zero to determine the critical points:
This implies:
This implies:
Together, these imply: