Question

firms s is the only producer of a particular type of foam fire retardant and insulation used in the construction of commercial buildings. the inverse demand equation for the product is p=1500-0.1q,where q is the annual sales quantity in tons and p is the price per ton. The firms total cost function(in dollar) is C=14000000+300Q+.05Q2

a.to maximize profit,how much foam insulation should firm S plan to produce and sell?What price should it charge?

b.Compute the firms total profit.

Answer 1

a. MR = MC to maximize profit, so:

MR = TR'(q) = 1500 - 0.2q,

MC = C'(q) = 300 + 0.1q,

1500 - 0.2q = 300 + 0.1q,

0.3q = 1200,

q = 4000 units,

p = 1500 - 0.1×4000 = 1100.

b. The firms total profit is:

$TP = 1100×4000 - (14000000 + 300×4000 + 0.05×4000^2) = -11600000.$