Question

7. The manager of a local restaurant has found that his cost function for producing coffee is C(x) = .097x, where C(x) is the total cost in dollars of producing x cups. (He is ignoring the cost of the coffeepot and the cost labor.) Find the total cost of producing the following numbers of cups of coffee. (a) 1000 cups (b) 1001 cups (c) What is the marginal cost for any cup? Let C(x) be the total cost in dollars to manufacture x items. Find the average cost in exercises 8 and 9.

Answer 1

To solve for the total cost of producing the following numbers of cups of coffee:

`\begin{gathered} C(x)=0.097x \\ \end{gathered}`

where

`\begin{gathered} x=nu\text{mber of cups of coff}e \\ C(x)=total\text{ cost }in\text{ dollars of producing x cups} \end{gathered}`

(a) The total cost of producing 1000 cups =

`\begin{gathered} C(x)=0.097x \\ x=1000 \\ C(x)=1000(0.097)=\text{ \$97} \end{gathered}`

(b) The total cost of producing 1001 cups =

`\begin{gathered} C(x)=0.097x \\ x=1001 \\ C(x)=1001(0.097)=\text{ \$97}.097 \end{gathered}`

(c) The marginal cost for any cup = $0.097

marginal cost can be found by taking the derivative of the function

`\begin{gathered} C(x)=0.097x \\ C^1(x)=0.097=\text{ \$0.097} \end{gathered}`