A firm's demand function is P = 60 - 0.5Q
If fixed costs are 10 and variable costs are Q + 3 per unit, find the maximum profit.
A)420
B)651.5
C)21
D)531.5
E)19

Question

Quizplus · Accepted Answer

To find the maximum profit, we need to first find the total revenue and total cost functions. Total Revenue =Price x Quantity = P x Q
Substituting the demand function, we get TR = (60 - 0.5Q)Q = 60Q - 0.5Q^2
Total cost = Fixed cost + Variable cost = 10 + (Q+3)Q = Q^2 + 3Q + 10
Profit = Total Revenue - Total cost = 60Q - 0.5Q^2 - Q^2 - 3Q - 10
= -1.5Q^2 + 57Q - 10
To find the maximum profit, we take the derivative and set it equal to 0:
d(Profit)/dQ = -3Q + 57 = 0
Q = 19
Substituting Q back into the profit function, we get the maximum profit:
Profit = -1.5(19)^2 + 57(19) - 10 = 531.5
Therefore, the best choice is D.

A Firm's Demand Function Is P = 60 - 0