Question

100 points!!!

“The revenue equation for a certain brand of toothpaste is y=2.6x, where X is the number of toothpaste sold and y is the income for selling X tubes. Cost equation is y=X+2000, where X is the number of tubes of toothpaste manufactured and y is the cost of producing X tubes. The following set of axis shows the graph of the cost and revenue equations. For what X-values will the company make a profit”

The company will make a profit for X-values: (greater than, less than, or equal to) ____?

Answer 1

The revenue equation is y=2.6x,

cost equation is y=x+2000

When the company makes profit only when revenue > cost

Lets frame inequality using revenue > cost

Replace the revenue equation and cost equation

Now solve the inequality for x

Subtract 1x from both sides

Divide both sides by 1.6

The company makes profit when x is greater than 1250

Explanation:

Answer 2

Greater than 1250

x > 1250

Explanation:

Base on the revenue equation and cost equation , we can infer that the company make a profit when x > 1250

Important Given Information:

The revenue equation is
`y=2.6x`

Cost equation is
`y = x+2000`

When the company makes profit only when:
`revenue > cost`

Let's frame inequality using:
`revenue > cost`

Replace the revenue equation and cost equation

`Revenue > Cost: 2.6x > + 2000`

Now Let's solve the inequality for x

`2.6x > 1x + 2000`

`2.6x - 1x > 2000`
`[2.6x-1x=1.6x]`

`1.6x > 2000`

Divide both sides by 1.6 ( what you do on one side do to the other)

`(1.6x)/(1.6)=(2000)/(1.6)`

`x >1250`

Hence, the company makes profit when x is greater than 1250

[RevyBreeze]