If the total revenues of a firm can be expressed as TR 30Q23

If the total revenues of a firm can be expressed as TR= 30Q-2.30Q^2 and Total Costs as TC= $12+6Q+.7Q^2 A) Need to determine the profit maximizing quantity B) Amount of maximum profit

Solution

(A)   TR= 30Q -2.30Q²

        TC= 12+ 6Q +.7Q²

Profit = TR - TC = (30Q -2. 30Q²) - (12+ 6Q +0.7Q²)

        = 30Q - 2.30Q² - 12 - 6Q - 0.7Q²

       = 30Q - 3Q² - 6Q -12

Profit will be maximum when first derivative of profit function = 0

d(profit)/dQ = 30 - 6Q - 6 = 0

                 => 24 -6Q =0

                 => 6Q = 24

                 => Q = 24/6 = 4

Therefore, the profit maximizing quantity is 4

(B) Profit = 30Q - 3Q² - 6Q -12

              =30(4) - 3(4)² - 6(4) -12

              = $36

Therefore, the amount of profit is $36