Question

A large company in the communication and publishing industry has quantified the relationship between the price of one of its products and the demand for this product as

Price = 140-0.02xDemand for an annual printing of this particular product. The fixed costs per year​ (i.e., per

​printing) = $46,000 and the variable cost per unit = $50.

What is the maximum profit that can be​ achieved? What is the unit price at this point of optimal​ demand? Demand is not expected to be more than $3,000

units per year.

a) The maximum profit that can be achieved is $...................

b) The unit price at the point of optimal demand is $..... per unit

(part A that I got 55250 is correct but I do not know how to do part B.

Thanks for your help

(engineering economy)

Answer 1

a)

Demand curve is given by

P=140-0.02x

Total Revenue=TR=P*x=140x-0.02x²

Total Cost is given by

TC=46000+50x

Profit=PR=TR-TC=140x-0.02x²-46000-50x=-46000+90x-0.02x²

dPR/dx=90-0.04x

Set dPR/dx=0 for profit maximization

90-0.04x=0

x=2250

Maximum profit is attained at x=2250. So

Maximum profit=-46000+90*2250-0.02*2250² =$55250

b)

We are given that

Price=140-0.02x

So, price at x=2250 is given by

Price=140-0.02*2250=$95 per unit