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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!

Respuesta :

MrRoyal

Answer:

[tex]c(x) =400 + 3x[/tex]

[tex]r(x) = 12x[/tex]

[tex]x = 44.44[/tex]

Explanation:

Given

Cost

[tex]Equipment = 400[/tex]

[tex]Production = 3[/tex] per mouse pad

Revenue

[tex]Sales\ Price = 12[/tex]

Solving (a): The cost function

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

[tex]c(x) =Equipment + Production * x[/tex]

[tex]c(x) =400 + 3 * x[/tex]

[tex]c(x) =400 + 3x[/tex]

Solving (b): The revenue function

Represent this with r(x)

[tex]r(x)= Sales\ Price * x[/tex]

[tex]r(x)= 12 * x[/tex]

[tex]r(x)= 12 x[/tex]

Solving (c): The break-even point

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

So, we have:

[tex]12x = 400 + 3x[/tex]

Collect Like Terms

[tex]-3x+12x = 400[/tex]

[tex]9x = 400[/tex]

Solve for x

[tex]x = \frac{400}{9}[/tex]

[tex]x = 44.44[/tex]