A machine shop has a setup cost of $3000 for the production of a new product. The cost, C, of labor and material for producing each unit is $10.75. The average cost function for producing x units is given by $\bar { C } = C / x$ . Determine the domain of the average cost function.
A)all real numbers
B)all $x 10.75$
C)all $x \neq 0$
D)all integers $x 0$
E)all integers $x 3000$

Question

A machine shop has a setup cost of $3000 for the production of a new product. The cost, C, of labor and material for producing each unit is $10.75. The average cost function for producing x units is given by $\bar { C } = C / x$ . Determine the domain of the average cost function.
A)all real numbers
B)all $x > 10.75$
C)all $x \neq 0$
D)all integers $x > 0$
E)all integers $x > 3000$

Quizplus · Accepted Answer

The setup cost of $3000 is a one-time fixed cost and is not affected by the number of units produced. The cost of labor and material for each unit is $10.75. Therefore, the total cost of producing x units is given by 
C(x) = 3000 + 10.75x 
The average cost function is given by 
$\bar { C } = \frac { C(x) }{ x } = \frac { 3000 }{ x } + 10.75$
The domain of the average cost function is all positive integers greater than 0, because the average cost function is not defined for x=0. Therefore, the best choice is D, all integers x >0.

A Machine Shop Has a Setup Cost of $3000 for the Production