   Chapter 10, Problem 7CS Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203

Solutions

Chapter
Section Finite Mathematics and Applied Cal...

7th Edition
Stefan Waner + 1 other
ISBN: 9781337274203
Textbook Problem

Because of intense lobbying by the utility industry, you are asked to revise the proposed policy so that the utility industry will pay no charge if sulfur emissions are reduced by the desired 10 million tons. How can you accomplish this?

To determine

To calculate: The revised proposal of policy so that no charge must be paid by utility industry because of intense lobbying by them if sulfur emissions are reduced by the 10 million tons from the current level of 25 million tons and the table shows the marginal cost of reducing sulfur emissions at various level of reduction.

 Reduction q(tons) 8,000,000 10,000,000 12,000,000 Marginal cost C′(q) 270 360 779
Explanation

Given Information:

The table shows the marginal cost of reducing sulfur emissions at various level of reduction.

 Reduction q(tons) 8,000,000 10,000,000 12,000,000 Marginal cost C′(q) 270 360 779

Formula used:

The derivative of function y=xn,n1 is;

dydx=nxn1

Calculation:

Consider the Emission charge, k×sulfur emissions.

Where k is the charges per ton of emissions.

The derivative of cost function at q=10,000,000 is 0 because the tangent line to the curve at this point has zero slope.

Consider the original level of sulfur emissions is 25 million tons. Evaluate q which represents the amount of reduction of emissions as;

q=25,000,000sulfur emissionssulfur emissions=25,000,000q

Then evaluate the annual sulfur emissions by multiplying both sides with k,

k×sulfur emissions=k(25,000,000q)=25,000,000kkq

Evaluate the total cost of emissions by adding cost of reducing emissions and total annual emission charge as;

D(q)=C(q)+25,000,000kkq

Now, evaluate the derivative of cost function is;

D(q)=ddqC(q)+ddq(25,000,000kkq)

Consider the function ddq(25,000,000kkq), where it is a linear function of q with slope k and intercept 25,000,000k

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