The manufacturer of a brand of mattresses will make x hundred units available in the market when the unit price is p = 150 + 70e^0.06x dollars.

Question

(a) Find the number of mattresses the manufacturer will make available in the market place if the unit price is set at $350/mattress. (Round your answer to the nearest integer.)

(b)

Use the result of part (a) to find the producers' surplus if the unit price is set at $350/mattress. (Round your answer to the nearest dollar.)

Answer 1

a) 350 = 150 + 70e^0.06x; x = ln(20/7)/0.06 = 17.50 hundred units.

b) PS = ∫₀^17.5(200 - 70e^0.06x)dx = (200x - 70/0.06e^0.06x)₀^17.5 = 3500 - 3333.92 = $166.07