C(Fix) linear function

Question

The manager of a restaurant found that the cost to produce 300 cups of coffee is $30.13, while the cost to produce 500 cups is $49.33. Assume the cost C(x) is a linear function of x, the number of cups produced. a. Find a formula for C(x)

b. The fixed cost is ____?

c. FInd the total cost of producing 1200 cups.

d. find the total cost producing 1201 cups

e. Find the marginal cost of the 1201st cup. f. What is the marginal cost of any cup and what does this mean to the manager?

Answer 1

there is a fixed cost that must be paid even if no cups of coffee are produced. call it F

 

there is a marginal cost for every cup produced. call it M

 

Therefore we can write two equations for cost C(x).

 

$30.13 = F + 300M

$49.33 = F + 500M

 

To solve for F and M, start by subtracting the first equation from the second equation. This will eliminate the variable F.

 

19.20 = 200M

M = .096 (this is equivalent to 9.6 cents)

 

Go back to one of the original equations, plug in the number .096 for M, and solve for F.

 

You should get 1.33

 

Now that you have values for F and M, you can write your cost equation.

 

C(x) = 1.33 + .096x

 

I will let you answer the remaining questions.