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?

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

you had 23.00$ because 28 - 5 = 23 then put it in dollar form