# 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...

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

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### 1 Answer

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)

= -q^3-150*q^2+60000*q-800

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