Unformatted Attachment Preview
79. 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 company
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.
a. Determine how to minimize the bus company’s
salary, hiring, and firing costs over the next five years.
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.
a. Determine the cheapest way of producing today’s
batch of NasaMist.
8881. A bank is attempting to determine where to invest its
assets during the current year. At present, $500,000
is 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
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.
a. Determine how to maximize the government’s
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.