Dr. Michael Tan is a renown dental surgeon with a reputation for being one of the best in reconstructive dental surgery. Dr. Tan enjoys a rather substantial degree of market power in this market. The estimated direct demand function for his services is:

Q = 600 0.25P

where Q is the number of dental surgeries performed monthly and P is the price of a typical dental surgery.

The average variable cost function for reconstructive dental surgery is estimated to be:

AVC = 2Q² 11Q + 500

where AVC is average variable cost (measured in dollars), and Q is the number of operations per month. Dr. Tan's fixed costs each month are $12,000.

Question:

If Dr. Tan aims to maximize his profit, how many surgeries should he perform each month?

[Hints:First find the total cost (TC) function as the sum of total variable cost andtotal fixed cost.Thenderivethemarginalcost(MC)functionas