Problems 6
1. The Westchester Chamber of Commerce periodically sponsor public service seminars
and programs. Currently, promotional plans are under way for this year’s program.
Advertising alternatives include television, radio, and news paper. Audience
estimates, cost, and maximum media usage limitations are shown.
Constraint
Television
Radio
Newspaper
Audience per advertisement
100,000
18,000
40,000
Cost per advertisement
$2000
$300
$600
Maximum media usage
10
20
10
To ensure a balanced use of advertising media, radio advertisements must not exceed
50% of the total number of advertisements authorized. In addition, television should
account for at least 10% of the total number of advertisements authorized.
a. If the promotional budget is limited to $18,200, how many commercial messages
should be run on each medium to maximize total audience contact? What is the
allocation of the budget among the three media, and what is the total audience
reached?
b. By how much would audience contact increase if an extra $100 were allocated to
the promotional budget?
2. Ajax Fuels Inc. is developing a new additive for air plane fuels. The additive is
mixture of three ingredients: A, B, and C. For proper performance, the total amount
of additive (amount of A + amount of B + amount of C) must be at least 10 ounces
per gallon of fuel. However, because of safety reason, the amount of additive must
not exceed 15 ounces per gallon of fuel. The mix or blend of the three ingredients is
critical. At least 1 ounce of ingredient A must be used for every ounce of ingredient
B. The amount of ingredient C must be used for every ounce of ingredient A. If the
costs per ounce for ingredients A,B, and C are $0.10, $0.03, and 0.09, respectively,
find the minimum cost mixture A,B, and C for each gallon of airplane fuel.
3. As part of the settlement for a class action lawsuit, How worth Corporation must
provide sufficient cash to make the following annual payment (in thousand dollars)
Year
1
2
3
4
5
6
Payment
190
215
240
285
315
400
The annual payments must be made at the beginning of each year. The judge will
approve an amount that, along with earning on its investment, will cover the annual
payments. Investment of the fund will be limited to savings (at 4% annually) and
government securities, at price and rates currently quoted in The Wall Street Journal.
Horxworth wants to develop a plan for making the annual payments by investing
in the following securities (par value=$1000). Funds not invested in three securities
will be placed in saving
Assume that interest is paid annually. The plan will be submitted to the judge and, if
approved. Horxworth will be required to pay trustee the amount that will be required
to fund the plan.
Security
1
2
Current Price
$1055
$1000
Rate (%)
6.750
5.125
Year to maturity
3
4
a. Use the linear programming to find the minimum cash settlement necessary to
fund the annual payments.
b. Use the dual price to determine how much more Horxworth should be willing to
pay now to reduce the payment at the beginning of year 6 to $400,000.
c. Use the dual price to determine how much more Horxworth should be willing to
pay to reduce the year 1 payment to $150,000.
d. Suppose that the annual payments are to be made at the end of each year.
Reformulate the model to accommodate this change. How much would
Horxworth save if this change could be negotiated?