The cost of controlling emissions at a firm rises rapidly as the amount of emissions reduced increases. We have the possible model, C(q) = 1,000 + 100q2 where q is the reduction in emissions (in pounds of pollutant per day) and C is the daily cost (in dollars) of this reduction. (a) If a firm is currently reducing its emissions by 10 pounds each day, what is the marginal cost of reducing emissions further? $ per one pound reduction in daily emissions (b) Government clean-air subsidies to the firm are based on the formula S(q) = 500q, where q is again the reduction (in pounds per day) and S is the subsidy (in dollars). At what reduction level does the marginal cost surpass the marginal subsidy? pounds of pollutant per day (c) Calculate the net cost function, N(q) = C(q) − S(q), given the cost function and the subsidy above. N(q) = Find the value of q that gives the lowest net cost. pounds of pollutant per day What is this lowest net cost? $ per day Compare your answer to that for part (b) and comment on what you find. This value is ---Select--- greater than smaller than equal to q in part (b).
The cost of controlling emissions at a firm rises rapidly as the amount of emissions reduced increases. We have the possible model, C(q) = 1,000 + 100q2 where q is the reduction in emissions (in pounds of pollutant per day) and C is the daily cost (in dollars) of this reduction. (a) If a firm is currently reducing its emissions by 10 pounds each day, what is the marginal cost of reducing emissions further? $ per one pound reduction in daily emissions (b) Government clean-air subsidies to the firm are based on the formula S(q) = 500q, where q is again the reduction (in pounds per day) and S is the subsidy (in dollars). At what reduction level does the marginal cost surpass the marginal subsidy? pounds of pollutant per day (c) Calculate the net cost function, N(q) = C(q) − S(q), given the cost function and the subsidy above. N(q) = Find the value of q that gives the lowest net cost. pounds of pollutant per day What is this lowest net cost? $ per day Compare your answer to that for part (b) and comment on what you find. This value is ---Select--- greater than smaller than equal to q in part (b).
Algebra and Trigonometry (MindTap Course List)
4th Edition
ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 4.2E: bThe average rate of change of the linear function f(x)=3x+5 between any two points is ________.
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Question
The cost of controlling emissions at a firm rises rapidly as the amount of emissions reduced increases. We have the possible model,
C(q) = 1,000 + 100q2
where q is the reduction in emissions (in pounds of pollutant per day) and C is the daily cost (in dollars) of this reduction.
(a)
If a firm is currently reducing its emissions by 10 pounds each day, what is the marginal cost of reducing emissions further?
$ per one pound reduction in daily emissions
(b)
Government clean-air subsidies to the firm are based on the formula
S(q) = 500q,
where q is again the reduction (in pounds per day) and S is the subsidy (in dollars). At what reduction level does the marginal cost surpass the marginal subsidy?
pounds of pollutant per day
(c)
Calculate the net cost function, N(q) = C(q) − S(q), given the cost function and the subsidy above.
N(q) =
Find the value of q that gives the lowest net cost.
pounds of pollutant per day
What is this lowest net cost?
$ per day
Compare your answer to that for part (b) and comment on what you find.
This value is ---Select--- greater than smaller than equal to q in part (b).
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