2. Appalachian Coal Mining believes that it can increase labor productivity and, therefore, net revenue by reducing air pollution in its mines. It estimates that the marginal cost function for reducing pollution by installing additional capital equipment is
MC = 40P
where P represents 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?
4. Twentyfirst 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.
|
Number of security guards
|
Number of radios stolen per week
|
|
0
|
50
|
|
1
|
30
|
|
2
|
20
|
|
3
|
14
|
|
4
|
8
|
|
5
|
6
|
a. If each security guard is paid 5200 a week and the cost of a stolen radio is 525, how many security guards should the firm hire?
b. If the cost of a stolen radio is 525, what is the most the firm would be willing to pay to hire the first security guard?
c. If each security guard is paid 5200 a week and the cost of a stolen radio is 550, how many security guards should the firm hire?