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In: Economics

A large wood products company is negotiating a contract to sell plywood overseas. The fixed cost...

A large wood products company is negotiating a contract to sell plywood overseas. The fixed cost that can be allocated to the production of plywood is $900,000 per month. The variable cost per thousand board feet is $131.50. The price charged will be determined by p = $600 – (0.05)D per 1,000 board feet. For this situation, (a) determine the optimal monthly sales volume for this product and calculate the profit (or loss) at the optimal volume. (b) What is the domain of profitable demand during a month?

Solutions

Expert Solution

Given:

Price:    p = $600 – (0.05) D   

Fixed cost:          Cf = $900,000/month

Variable cost:    Cv = $131.50/unit

The unit demand (D) is 1,000 board feet

Calculation:

(a) Optimal monthly sales volume:

D* = 4,685 units/month

Profit (or loss) at the optimal volume:

Total Revenue = 600D – 0.05 D2 (Price * Quantity)

(substitute D* value)

Total revenue = [(600*4685) - 0.05*(4685)2] = [28,11,000 - 10,97,461.25]

Total revenue = 17,13,538.75

Total Cost = 900,000 + 131.50D (Fixed cost + Variable cost)

Total cost = [900,000 + (131.50*4685)] = 900,000 + 6,16,077.5

Total cost = 15,16,077.5

Profit = Total Revenue ‐ Total Cost

Profit = 1713538.75 - 1516077.5

Profit = 197,461.25 /month

(b) Domain of profitable demand during a month:

Profit = TR - TC = 0

Profit = 600D – 0.05 D2 -  900,000 + 131.50D = 0

=  ‐0.05D2 +600D ‐ 900,000 – 131.50D

=  ‐0.05D2 + 468.50D – 900,000

Range of profitable demand is 2,698 units to 6,672 units per month.

Break even points
D1= 2697.8 and D2= 6672.3 units per month. Range of profitable demand is 2697.8-6672.3 units.

Rahul Sunny answered 2 years ago
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