TABLE 10. Combinations of Plans A, B, and C (multiply
all values in table by 1000)
Individual investment, $
Combination of plans
A and B Plan C Annual dividend, $
600 O 135+ 0-135
500 100 116+ 15 = 131
400 200 91+ 31 = 122
300 300 63+ 48 = 111
200 400 44+ 56=100
100 500 25+ 79=104
O 600 0+102=102the dividend from plan C is $31,000. Thus, the total dividend is $91,000 + $31,000 =
$122,000. Table 10 shows that the maximum possible dividend is $135,000.
- Identify the most profitable combination of all three plans
From Table 10, the most profitable combination results from placing $600,000 in the A-B
combination and nothing in plan C. From Table 9, the A-B combination consists in plac-
ing $200,000 in A and $400,000 in B. Thus, the most profitable way of dividing the capi-
tal is $200,000 in plan A, $400,000 in plan B, and nothing in plan C.
Related Calculations: This problem can be solved directly by forming all possi-
ble combinations of plans A, B, and C and computing their annual dividends; the number
of combinations is 28. However, where the number of combinations is very large, the di-
rect method becomes unwieldy. Dynamic programming provides a systematic way of
solving the problem, and it reduces the number of calculations. It will be applied again in
a later calculation procedure.
ECONOMIC LEVEL OF INVESTMENT
A firm planned to purchase and improve property in the expectation that land values in
the area would appreciate in the near future. The question arose as to how large an invest-
ment should be made. The following data were compiled for five alternative plans, each
representing a different level of investment.
Plan
ABCDE
Investment^ 200,000 270,000 340,000 410,000 460,000
Rate of return, % 14.1 13.8 12.5 11.6 12.3If 12 percent is considered the minimum acceptable rate of return, determine the most at-
tractive plan.