Question

The cost, in dollars, of manufacturing x microwaves is 6,000 + 300x dollars. The amount received when selling these x microwaves is 700x dollars. What is the least number of microwaves that must be manufactured and sold so that the net profit is $2400?

Answer 1

21 microwaves

Explanation:

The net profile is equal to the income less the total cost, so the equation to the net profile NP is:

NP = 700x - (6000 + 300x)

Where 700x is the income and (6000+300x) is the cost of manufacturing.

Now, replacing NP by 2400 and solving for x, we get:

2400 = 700x - (6000 + 300x)

2400 = 700x - 6000 - 300x

2400 + 6000 = 400x

8400 = 400x

`(8400)/(400)=x\\ 21=x`

So, the least number of microwaves that must be manufactured and sold so that the net profit is $2400 is equal to 21.