The cost of controlling emissions at a firm rises rapidly as the amount of emiss

Question

The cost of controlling emissions at a firm rises rapidly as the amount of emissions reduced increases. Here is a possible model:

C(q) = 4,200 + 99q2

where q is the reduction in emissions (in pounds of pollutant per day) and C is the daily cost to the firm (in dollars) of this reduction. What level of reduction corresponds to the lowest average cost per pound of pollutant? (Round your answer to two decimal places.)
pounds of pollutant per day

What would be the resulting average cost to the nearest dollar?
$  per pound

Explanation / Answer

The Average Cost, A(q) = C(q)/q = 4200/q + 99q

Take the derivative of A(q) and set it to 0:

A'(q) = -4200/q^2 + 99

=> q=6.51 (only positve root)= pounds per day.

For second part.

Plug in value of 'q' in A(q).

A(6.51) = 4200/6.51 + 99(6.51)

= $1289.65 per pound.

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