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FINANCIAL APPLICATIONS 177

Figure 4.9 The Management Scientist Solution for the Hewlitt Corporation Cash
Requirements Problem
EXCEL file Objective Function Value = 1728.79385
HEWLITT
Variable Value Reduced Costs
-------------- --------------- -----------------
F 1728.79385 0.00000
B1 144.98815 0.00000
B2 187.85585 0.00000
B3 228.18792 0.00000
S1 636.14794 0.00000
S2 501.60571 0.00000
S3 349.68179 0.00000
S4 182.68091 0.00000
S5 0.00000 0.06403
S6 0.00000 0.01261
S7 0.00000 0.02132
S8 0.00000 0.67084
Constraint Slack/Surplus Dual Prices
-------------- --------------- -----------------
1 0.00000 -1.00000
2 0.00000 -0.96154
3 0.00000 -0.92456
4 0.00000 -0.88900
5 0.00000 -0.85480
6 0.00000 -0.76036
7 0.00000 -0.71899
8 0.00000 -0.67084

The solution also shows that E636 148 (see S 1 ) will be placed in savings at
thebeginning of thefirst year.Bystartingwith E1,728 794, the company
can make the specified bond and savings investments and have enough left over
to meet the retirement programme’s first-year cash requirement of E430 000.
The optimal solution in Figure 4.9 shows that the decision variables S 1 , S 2 , S 3 and
S 4 are all greater than zero, indicating investments in savings are required in each of
the first four years. However, interest from the bonds plus the bond maturity
incomes will be sufficient to cover the retirement programme’s cash requirements
in years 5 through 8.
The dual prices have an interesting interpretation in this application. Each right-
hand side value corresponds to the payment that must be made in that year. Note that
the dual prices are negative, indicating that reducing the payment in any year would be
beneficial because the total funds required for the retirement programme’s obligation
would be less. Also note that the dual prices show that reductions are more beneficial in
the early years, with decreasing benefits in subsequent years. As a result, Hewlitt would
benefit by reducing cash requirements in the early years even if it had to make
equivalently larger cash payments in later years.
In this application, the dual price can be thought of as the negative of the present
value of each euro in the cash requirement. For example, each euro that must be
paid in year 8 has a present value of E0.67084.

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