A manufacturer has determined that the total cost c of producing q units of a product is given by Average cost will be a minimum at a production level of
A) 100 units.
B) 200 units.
C) 400 units.
D) 800 units.
E) none of the above

Question

A manufacturer has determined that the total cost c of producing q units of a product is given by  Average cost will be a minimum at a production level of
A) 100 units. 
B) 200 units. 
C) 400 units. 
D) 800 units. 
E) none of the above

Quizplus · Accepted Answer

To find the minimum average cost, we need to find the derivative of the cost function with respect to q and set it equal to zero.

c = 1500 + 6q + 0.01q^2

Taking the derivative with respect to q:

c' = 6 + 0.02q

Setting c' equal to zero and solving for q:

6 + 0.02q = 0 
0.02q = -6 
q = -300

Since a negative production level doesn't make sense, we reject this solution. The only other critical point is a minimum at q = 300, but we need to check if it's indeed a minimum.

Taking the second derivative:

c'' = 0.02

Since c'' is positive, we have a minimum at q = 300. Therefore, the best choice is C, 400 units.

A Manufacturer Has Determined That the Total Cost C of Producing