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The cost of controlling emissions at a firm is given by C(q) = 4,000 + 100q2 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. Government clean-air subsidies amount to $400 per pound of pollutant removed. How many pounds of pollutant should the firm remove each day in order to minimize net cost (cost minus subsidy)?

Respuesta :

Answer:

2 pounds of reduction per pollutant per day

Step-by-step explanation:

Cost of controlling emissions  :  C(q)  =  4000 + 100*q

And govermment subside is 400 * q

Therefore the cost function is:

C(q) =  4000 + 100q² - 400q

Derivative of C(q)   ⇒ C´(q)  =  200q - 400

equalizing to cero    200*q - 400 = 0  ⇒  q  = 400/200   q = 2

If we take second derivative  C¨¨(q)  = 200        200> 0  there is a minimun in the poin q = 2

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