Question

1. A company produces circuit boards used to upgrade computer equipment. The fixed cost is $42,000 per month, and the variable cost is $53 per circuit board. The selling price per unit isP=$150 – 0.02D. Maximum output of the plant is 4,000 units per month.

1. Determine the optimal demand for this product.
2. What is the maximum profit per month?
3. At what volume does breakeven occur?
4. What is the company’s range of profitable demand?

Answer 1

(a)

Demand is optimal and profit is maximized when MR = MC = $53.

Total revenue (TR) = P x D = 150D - 0.02D²

MR = dTR/dD = 150 - 0.04D

150 - 0.04D = 53

0.04D = 97

D = 2,425

(b)

When D = 2,425, P = 150 - (0.02 x 2,425) = 150 - 48.5 = 101.5

TR = 101.5 x 2,425 = 246,137.5

TC = FC + TVC = 42,000 + (53 x 2,425) = 42,000 + 128,525 = 170,525

Profit = TR - TC = 246,137.5 - 170,525 = 75,612.5

(c)

At break-even, TR = TC.

If break-even quantity be D, then

150D - 0.02D² = 42,000 + 53D

0.02D² - 97D + 42,000 = 0

Solving this quadratic equation using online solver,

D = 0 or D = 4,850

(d)

Demand is profitable when Profit > 0.

When D = 4,850, Profit = 0. Therefore, Profitable range of demand is:

0 < D < 4,850