The cost of controlling emissions at a firm rises rapidly as the amount of emissions reduced increases. Here is a possible model:
C(q) = 1,500 + 190q^2
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
C(q) = 1,500 + 190q^2
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
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The Average Cost, say A(q) is C(q)/q = 1500/q + 190q
Take the derivative of A(q) and set it to 0:
-1500/q^2 + 190 = 0
q^2 = 1500/190
q = sqrt(150/19)
Plug-in q = sqrt(150/19) into A(q) to get the 2nd answer.
Take the derivative of A(q) and set it to 0:
-1500/q^2 + 190 = 0
q^2 = 1500/190
q = sqrt(150/19)
Plug-in q = sqrt(150/19) into A(q) to get the 2nd answer.