Algebra Word Problem

Question

A company has determined that the demand function for a certain couch is given by p=2700-0.75x, where p is the price per couch, and x is the number of couches sold. The fixed costs associated with producing a line of couches is $760,000, and each couch costs $360 to make. Determine how many couches should be manufactured and sold in order to maximize profit. Start by finding functions to represent the revenue and the total cost, then find a function for profit.

Answer 1

C = 760000+360x

p = 2700-3x/4

R = px = 2700x -.75x^2

Profit = R-C = -.75x^2 +2340x - 760000

take the derivative and set = 0

-1.5x +2340 = 0

x = 2340/1.5 = profit maximizing output

= 1560 couches