Woodland Instruments Inc operates in the highly competitive

Woodland Instruments, Inc. operates in the highly competitive electronics industry. Prices for its RD – D2 control switches are stable at $100 each. Engineering estimates that total costs for each RD – D2 control switch are: TC = $500,000 + $25Q + $0.0025Q^2

TR = $100Q

Part a – Calculate the profit maximizing level of output

Part b – Calculate maximum profit

Solution

a. Profit maximizing level is at that quantity where Marginal Revenue = Marginal Cost

MR = d/dQ (TC) = 25 + 2 * 0.0025Q = 25 + 0.0050Q
MC = d/dQ (TR) = 100

25 + 0.0050Q = 100
0.005Q = 75
Q = 75/0.005 = 15,000

d. Profit = Total revenue - total cost

= 100 * 15000 - (500000 + 25*15000 + 0.0025 * 15000 * 15000)
= 1,500,000 - (500,000 + 375,000 + 562,500)
= 1,500,000 - 1437500 = $62,500