Question

A business has determined they will 150 items if they charge $40 per item. It has

also been determined that if the price is increased to $45, then only 100 items
will be sold.
a) Write the linear function in slope-intercept form that determines the number of
items sold.
b) What is the price per item that will maximize revenue? $
c) How many items will be sold at that price?
DD) What is the maximum revenue of the company? $

Answer 1

a) y=45x (is $45 is charged per item), or y=40x (if $40 per item)

b) $40

c) 150

d) $6000

Explanation:

a) The slope would be either 45 or 40, depending on which equation you write. We know this because the cost is the slope per item, so the rise over run is over one.

b) To find which one makes more money, we have to determine the total profit from each outcome. We can do this by solving 45x100=a, and 40x150=b. The first equation represents the profit if the price is $45, while the second represents the outcome if they charge $40 per item. a=4500, while b=6000, so $40 per item would bring them more revenue.

c) The number of items sold at the price of $40 is 150, the problem tells us this.

d) Because $40 per item is their higher profit, the maximum revenue is $6000.