A company has established that the relationship between the sales price for one

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 90-0.3D (D is the demand or quantity sold per month and p is the price in dollars) The fixed cost is $900 per month and the variable cost is $20 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? a. The maximum profit per month for this product is s(Round to the nearest dollar.)

Explanation / Answer

Consider the given problem here the demand curve is given by, “P=90-0.3*Q”. Now, the cost function is given by, “C=900+20*Q”.

So, the profit function is given by, “A = P*Q - C = (90 - 0.3*Q)*Q – (900+20*Q).

=> A = (90 - 0.3*Q)*Q – (900+20*Q) = 90*Q - 0.3*Q^2 – 900 - 20*Q. SO, the FOC for maximization is given by.

=> dA/dQ = 0, => 90 - 0.6*Q - 20 = 0, => 70 = 0.6*Q, => Q = 116.67.

So, here the optimum price is given by, “P = 90-0.3*Q = 90-0.3*116.67 = 55 = P.

SO, the optimum profit is given by, “A= P*Q-C = 55*116.67 - (900+20*116.67) = 6,416.85 – 3,233.4 = 3,183.45.

So, here the maximum profit is given by, “$3,183” per month and the profitable demand is given by, “D=116.67”.

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