Question

​Raggs, Ltd. a clothing​ firm, determines that in order to sell x​ suits, the price per suit must be p. It also determines that the total cost of producing x suits is given by . ​a) Find the total​ revenue, . ​b) Find the total​ profit, . ​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

Answer:

a. Total revenue = Number of units sold * price of suit

= x * (140 - 0.5x)

= 140x - 0.5x²

b. Total profit = Revenue - Costs

= 140x - 0.5x² - (2000 + 0.75x²)

= 140x - 2,000 - 1.25x²

c. The profit is maximized at a quantity where the derivative of the profit function equals zero.

Derivative = 140 - 2.5x

Maximized profit ;

140 - 2.5x = 0

2.5x = 140

x  = 56 suits

d. Maximum profit using the profit function;

= 140x - 2,000 - 1.25x²

= (140 * 56) - 2,000 - (1.25 * 56²)

= 7,840 - 2,000 - 3,920

= $1,920

e. Price per suit;

= 140 - 0.5x

= 140 - 0.5 * 56

= $112 per suit