Solve the problem below.

Quadratic Equations.

For certain company, the cost for producingx

items is40x+300

and the revenue for sellingx

items is80x0.5x

2

.

The profit that the company makes is how much it takes in (revenue) minus how much it spends (cost). In economic models, one typically assumesthat a company wants to maximize its profit, or at least wants to make a profit!

Part a: Set up an expression for the profit fromproducing and sellingx

items. We assume that the company sells all of the items that it produces. (Hint: it is a quadratic polynomial.)

Part b: Find two values ofx

that will create a profit of$300

.

The field below accepts a list of numbers or formulas separated by semicolons (e.g.2;4;6

orx+1;x1

). The order of the list does not matter. To entera

, type sqrt(a).

x=

Part c: Is it possible for the company to make a profit of$15,000

?