Question

A manufacturer has a monthly fixed cost of $60,000 and a production cost of $10 for each unit produced. The product sells for $15/unit.A.) what is the cost function?B.) what is the revenue function?C.) what is the profit function?D.) compute the profit (loss) corresponding to production levels of 10,000 and 14,000 units/months

Answer 1

Given the word problem, we can deduce the following information:

Fixed Cost = $60,000

Production Cost = $10 for each unit produced

To solve the following based on the given information, we let x be the number of units. So,

a)

The get the cost function, we note first that the cost would be:

Cost = Fixed Cost + Production Cost per unit produced

Hence, the cost function is:

C(x)=60,000+10x

b)

The revenue is the gross sales, so the revenue function would be:

R(x) = 15x

c)

We also note that the formula to get the profit is:

Profit= Revenue - Cost

So the profit function would be:

P(x)= 15x-(60,000+10x) = 15x-60,000-10x

Simplify

P(x)= 5x-60,000

d)

To compute the profit or loss, we plug in x=10,000 and x = 14,000 into the profit function:

When x =10,000:

`\begin{gathered} P(x)=5x-60000 \\ P(10000)=5(10000)-60000 \\ \text{Simplify} \\ P(10000)=-10,000 \end{gathered}`

It means that when x=10,000, there would be a $10,000 loss.

When x=14,000:

`\begin{gathered} P(x)=5x-60000 \\ P(14000)=5(14000)-60000 \\ \text{Calculate} \\ P(14000)=10000 \end{gathered}`

It means that when the production is 14,000 units/month, there would be a $10,000 profit.