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.
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%.
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.
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?
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.