Question

(40 Points) HURRY!

Games 'n' Mods is a large electronics company that builds and sells custom gaming computers. Research shows that customers pay more per computer when the company builds fewer computers. If the company builds q computers to sell, it can charge 800–5q dollars for each computer. This means its revenue will be q(800–5q) dollars. Each computer requires $300 in materials to build, and Games 'n' Mods has invested $8,000 in new equipment. This means the company's costs will be 300q+8,000 dollars. So, if the company builds and sells q computers, its profit will be q(800–5q)–(300q+8,000) dollars.
This expression can be simplified to 5q²+500q–8,000 and then written in factored form as 5(q–20)(q–80).
What do the numbers 20 and 80 represent in the expression?
Options are in the attachment.

Answer 1

Explanation:

The expression in factored form is 5(q-20)(q-80).

The numbers 20 and 80 represent the values of q that make the expression equal to zero.

Setting the expression equal to zero, we get:

5(q-20)(q-80) = 0

This means that either (q-20) = 0 or (q-80) = 0, since the product of two factors is zero if and only if at least one of the factors is zero.

Solving for q in each case, we get:

q-20 = 0 -> q = 20

q-80 = 0 -> q = 80

Therefore, the numbers 20 and 80 represent the values of q that make the profit equal to zero (i.e., the break-even points). If Games 'n' Mods builds and sells fewer than 20 or more than 80 computers, it will operate at a loss. If it builds and sells between 20 and 80 computers, it will make a profit.