the demand function for a product is p= 60000-50q dollars, and the average
function is AC=800/q+100q+q(square):
a) Determine the quantity that will maximize profit
b) Determine the selling price at the optimal quantity
c) Determine the minimize profit
The demand function for a product is p= 60000-50q and the average cost is given by: AC=800/q+100q+q^2.
If q items of the product are sold, the total cost is 800 + 100q^2 + q^3. The profit made is (60000q - 50q^2)-(800 + 100q^2 + q^3)
The quantity to maximize profit can be determined by solving (-q^3-150*q^2+60000*q-800)' = 0
-3q^2 - 300q + 60000 = 0
The positive root of this equation is q = 100
Selling 100 items of the product maximizes profit.
The maximum profit is $3499200
The selling prize at the optimal quantity is $55000