A bus company believes that it will need the following numbers of bus  drivers during each of the next five years: 60 drivers in year 1; 70  drivers in year 2; 50 drivers in year 3; 65 drivers in year 4; 75  drivers in year 5.

At the beginning of each year, the bus company  must decide how many drivers to hire or fire. It costs $4000 to hire a  driver and $2000 to fire a driver. A driver’s salary is $45,000 per  year. At the beginning of year 1 the com-pany has 50 drivers. A driver  hired at the beginning of a year can be used to meet the current year’s  requirements and is paid full salary for the current year.

• Determine how to minimize the bus company’s salary, hiring, and firing costs over the next five years.
• Use  SolverTable to determine how the total number hired, total number  fired, and total cost change as the unit hiring and firing costs each  increase by the same percentage.

Question 80

A  pharmaceutical company produces the drug NasaMist from four chemicals.  Today, the company must produce 1000 pounds of the drug. The three  active ingredients in NasaMist are A, B, and C. By weight, at least 8%  of NasaMist must consist of A, at least 4% of B, and at least 2% of C.  The cost per pound of each chemical and the amount of each active  ingredient in one pound of each chemical are given in the file  P14_80.xlsx. It is necessary that at least 100 pounds of chemical 2 and  at least 450 pounds of chemical 3 be used.

• Determine the cheapest way of producing today’s batch of NasaMist.
• Use  SolverTable to see how much the percentage of requirement of A is  really costing the company. Let the percentage required vary from 6% to  12%.

Question 81

A bank is  attempting to determine where to invest its assets during the current  year. At present, $500,000is available for investment in bonds, home  loans, auto loans, and personal loans. The annual rates of return on  each type of investment are known to be the following: bonds, 6%; home  loans, 8%; auto loans, 5%; personal loans, 10%. To ensure that the  bank’s portfolio is not too risky, the bank’s investment manager has  placed the following three restrictions on the bank’s portfolio: 

• The amount invested in personal loans cannot exceed the amount invested in bonds. 
• The amount invested in home loans cannot exceed the amount invested in auto loans. 
• No more than 25% of the total amount invested can be in personal loans.

Help the bank maximize the annual return on its investment portfolio.

Question 86

The  government is auctioning off oil leases at two sites: 1 and 2. At each  site 10,000 acres of land are to be auctioned. Cliff Ewing, Blake  Barnes, and Alexis Pickens are bidding for the oil. Government rules  state that no bidder can receive more than 40% of the land being  auctioned. Cliff has bid $10,000 per acre for site 1 land and $20,000  per acre for site 2 land. Blake has bid $9000 per acre for site 1 land  and $22,000 per acre for site 2 land. Alexis has bid $11,000 per acre  for site 1 land and $19,000 per acre for site 2 land.

• Determine how to maximize the government’s revenue.
• Use  SolverTable to see how changes in the government’s rule on 40% of all  land being auctioned affect the optimal revenue. Why can the optimal  revenue not decrease if this percentage required increases? Why can the  optimal revenue not increase if this percentage required decreases?

Question 89

Based  on Bean et al. (1987). Boris Milkem’s firm owns six assets. The  expected selling price (in millions of dollars) for each asset is given  in the file P14_89 .xlsx. For example, if asset 1 is sold in year 2, the  firm receives $20 million. To maintain a regular cash flow, Milkem must  sell at least $20 million of assets during year 1, at least $30 million  worth during year 2, and at least $35 million worth during year 3.  Determine how Milkem can maximize his total revenue from assets sold  during the next three years.