A coal producer has the following total cost: TC=$187,500+$5Q+$0.0003Q2, where Q is tons of coal produced per month. Calculate the firm’s maximum profit if coal price is stable at $20/ton. (7 points)

Question

A coal producer has the following total cost: TC=$187,500+$5Q+$0.0003Q2, where Q is tons of coal produced per month.  Calculate the firm’s maximum profit if coal price is stable at $20/ton. (7 points)

Fredr · Answer

Profit = revenue - TC Revenue = [Price] x [tons of coal] Take the first derivative of profit with respect to Q and set this equal to zero, then solve for Q.