A construction material company is planning to manufacture a new beam. The sales

Question

A construction material company is planning to manufacture a new beam. The sales department estimates that the quantity that can be sold depends on the selling price. As the selling price is increased, the quantity that can be sold decreases. They estimate: 1. P = $80.00-0.05 G where P selling price per beam and G = quantity of beams sold per year. The management estimates that the average cost of producing the beam decreases as the quantity sold increases. They estimate: Determine the number of beams the company should produce each year to maximize its profit (income minus cost and income is profit times quantity sold C $10.00 G + 5000 where C = cost to produce G beams per year.

Explanation / Answer

P=80-0.05 G where P is selling price per beam

so total revenue earned for G beam in one year = P*G= 80G-0.05G2

C=10G+5000 C: cost to produce G beam per year

Net profit p= PG-C = 80G-0.05 G2 -10G-5000

p=70G-0.05G2-5000

differntiate for maximization

dp/dG= 70 - 0.1G

for maximum value dp/dG = 0

G= 70/0.1 = 700

So the company should produce 700 new beam for maximum profit

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