Question

The manufacturing shop is producing custom photo imprinted mouse pads for clients. The startup equipment cost $400. A mouse pad has a production cost of $3. The retail sale is $12.

1). Write a cost function
2). Write a revenue function
3). Give the break-even point
Please help me answer all 3 questions, thanks!

Answer 1

`c(x) =400 + 3x`

`r(x) = 12x`

`x = 44.44`

Step-by-step explanation:

Given

Cost

`Equipment = 400`

`Production = 3` per mouse pad

Revenue

`Sales\ Price = 12`

Solving (a): The cost function

Let the number of mouse pad be x and the cost function be c(x).

`c(x) =Equipment + Production * x`

`c(x) =400 + 3 * x`

`c(x) =400 + 3x`

Solving (b): The revenue function

Represent this with r(x)

`r(x)= Sales\ Price * x`

`r(x)= 12 * x`

`r(x)= 12 x`

Solving (c): The break-even point

This is the point where r(x) = c(x)

So, we have:

`12x = 400 + 3x`

Collect Like Terms

`-3x+12x = 400`

`9x = 400`

Solve for x

`x = (400)/(9)`

`x = 44.44`