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Finding the optimal activity levels

1. Appalachian Coal Mining believes that it can increase labor productivity and, therefore, net revenue by reducing air pollution in its mines. Its estimates that the marginal cost function for reducing pollution by installing additional capital equipment is: MC = 40P where P represent a reduction of one unit of pollution in the mines. It also feels that for every unit of pollution reduction the marginal increase in revenue (MR) is MR = 1,000 - 10P. How much pollution reduction should Appalachian Coal Mining undertake?

2. Twenty first Century Electronics has discovered a theft problem at its warehouse and has decided to hire security guards. The firm wants to hire the optimal number of security guards. The following table shows how the number of security guards affects the number of radios stolen per week. If:

Number of Number of
security guards stolen radios per week
0 50
1 30
2 20
3 14
4 8
5 6

a. If each security guard is paid $200 a week and the cost of a stolen radio is $25, how many security guards should the firm hire?
b. If the cost of the stolen radio is $25, what is the most the firm would be willing to pay to hire the first security guard?
c. If each security guard is paid $200 a week and the cost of a stolen radio is $50, how many security guards should the firm hire?

Solution Preview

Please refer attached file for better clarity of tables.

Problem 1
Net revenue can be maximized by reducing the pollution level such that

MR=MC

1000-10P=40P

50P=1000

P=20

20 units of pollution should be reduced.

Problem 2

Number, N Number of radios stolen per week, Q Cost of Radio, P Total Loss, TS=P*Q Marginal Savings*
0 50 25 1250
1 30 25 750 500
2 20 25 500 250
3 14 ...

Solution Summary

There are two problems. Solutions to these problems explain the methodology to find the optimal activity levels.

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