Question

​Raggs, Ltd. a clothing​ firm, determines that in order to sell x​ suits, the price per suit must be pequals180 minus 0.5 x. It also determines that the total cost of producing x suits is given by Upper C (x )equals5000 plus 0.75 x squared. ​a) Find the total​ revenue, Upper R (x ). ​b) Find the total​ profit, Upper P (x ). ​c) How many suits must the company produce and sell in order to maximize​ profit? ​d) What is the maximum​ profit? ​e) What price per suit must be charged in order to maximize​ profit?

Answer 1

Step-by-step explanation:

(a) R(x) = x(150 - 0.75x) => 150x - 0.75x²

(b) P(x) = R(x) - C(x) => 150x - 0.75x² - (2000 + 0.75x²)

so, P(x) = 150x - 2000 - 1.5x²

(c) Now, P '(x) = 150 - 3x = 0....at maximum

i.e. when x = 50 suits

(d) P(50) = 150(50) - 2000 - 1.5(50)²

=> 7500 - 2000 - 3750

i.e. £1750

(e) price --> 150 - 0.75(50) => 150 - 37.5

Hence, price per suit is £112.50 in order to maximise profits.