143k views
0 votes
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!

User Lini Sax
by
3.0k points

1 Answer

11 votes

Answer:


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

User Drenocartero
by
3.1k points