A company has determined that the demand function for a certain couch is given by p = 3000 0.5x, 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 $700,000, and each couch costs $320 to make.

a. Find functions to represent the:

i. Revenue

ii. Total cost

iii. Profit.

b. Determine how many couches should be manufactured and sold in order to maximize profit.