Question

The Zinger Company manufactures and sells a line of sewing machines. Demand per period (Q) for a particular model is given by the following relationship: Q = 400-.5P where P is price. Total costs (including a "normal" return to the owners) of producing Q units per period are: TC = 20,000 + 50Q + 3Q2

(a) Express total profits (π) in terms of Q.

(b) At what level of output are total profits maximized?

(c) What price will be charged?

(d) What are total profits at this output level?

PLEASE ANSWER A, B, C, and D

Answer 1

(a) Q = 400 - 0.5P

0.5P = 400 - Q

P = 800 - 2Q

TR = P * Q = 800Q - 2Q²

TC = 20,000 + 50Q + 3Q²

Profit (π) = TR - TC

                = 800Q - 2Q² - (20,000 + 50Q + 3Q²)

                = 800Q - 2Q² - 20,000 - 50Q - 3Q²

            π = 750Q - 5Q² - 20,000

(b) Total profits maximized at the point where first order derivative of profit function is equal to 0.

750 - 10Q = 0

10Q = 750

Q = 750 / 10 = 75          [profit maximizing output]

(c) P = 800 - 2Q = 800 - 2(75) = $650

(d) Total Profit = 750Q - 5Q² - 20,000 = 750(75) - 5(75)² - 20,000 = 56,250 - 28,125 - 20,000 = $8,125