Question

A company has established that the relationship between the sales price for one of its products and the quantity sold per month is approximately p equals 75 minus 0.1 Upper Dp=75−0.1D ​(D is the demand or quantity sold per month and p is the price in​ dollars). The fixed cost is ​$1 comma 0001,000 per month and the variable cost is ​$3030 per unit produced. a. What is the maximum profit per month for this​ product? b. What is the range of profitable demand during a​ month?

Answer 1

Answer:

Q = 450

P = 35

Explanation:

TR = P x Q = (75 - 0.1Q) x Q = -0.1Q2 + 75Q

Then, Cost = (30Q + 1,000)

Profit: Total revenue - C

-0.1q2 + 75Q - 30q - 1,000 = -0.1q2  + 45q - 1,000

as this is a quadratic function we identify a b c:

a= -0.1 b = 45 x = -1000

the profit maximum point is at the vertex:

-b/2a = -45/ 2(-0.1) = -45/-0.1 = 450

The profit maximize at Q = 450

P = 75 - 0.1x450 = 35