ABX Clothing manufactures expensive jackets for sale to college stores in runs of up to 150. Its cost (in dollars) for a run of jackets is

() = + + .

, ( ≤ ≤ )

(a)ABX Clothing sells the jackets at $90 each. Find the revenue function.

(b) Find the profit function.

(c) How many should ABX Clothing manufacture to make a profit? (Round your answer up to

the nearest whole number.)

a. R(x) = 90x b. -1500 -10x - 0.2x c. 148

Step-by-step explanation:

a. Since we have x jackets produced at a rate of  $90 per jacket, the revenue function, R(x) = rate × number of jackets = 90 × x = 90x

R(x) = 90x

b. Since the cost function is C(x) = 1500 + 100x + 0.2x, the profit function P(x) = Revenue function - cost function = R(x) - C(x) = 90x - (1500 + 100x + 0.2x)

P(x) = -1500 + 90x - 100x - 0.2x

P(x) = -1500 - 10x - 0.2x

c. For a profit, P(x) > 0

-1500 - 10x - 0.2x > 0

0.2x + 10x + 1500 < 0

10.2x + 1500  < 0

10.2x < -1500

x < -1500/10.2

x < -147.05

x < -147

So, ABX Clothing needs to produce greater than 147 jackets to make a profit. So, they need to make 148 jackets to make a profit.

47 - 90 = 43

43 - 180 = x

x = 137