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

Answer:

$c(x) =400 + 3x$

$r(x) = 12x$

$x = 44.44$

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

$x = \frac{400}{9}$

$x = 44.44$