The board of directors of General Wheels Co. is considering seven large capital
ID: 329795 • Letter: T
Question
The board of directors of General Wheels Co. is considering seven large capital investments. Each inv only once These investments differ in the estimated long-run profit that they will generate as well as required, as shown by the following table. investment can in the amount of capita Investment Estimated Profit Capital Required Opportunity (millions) (millions) $17 10 15 19 $43 28 34 48 17 32 23 4 6 13 9 The total amount of capital available for these investments is $100 million. Investment opportunities 1 and 2 are mutually exclusive, and so are 3 and 4. Furthermore, neither 3 nor 4 can be undertaken unless one of the first two opportunities is of capital investments that witt maximize the total estimated long-run Develop a mathematical model for this problem. are no such restrictions on investment opportunittes 5, 6, and 7. The objective is to select the combination profit -undertaExplanation / Answer
This is a knapsack problem with some additional constraints.
Define Xj = 1 if investment opportunity #j is selected, and 0 otherwise.
Then the objective is
Maximize 17X1 + 10X2 + 15X3 + 19X4 + 7X5 + 13X6 + 9X7
and the budget constraint is 43X1 + 28X2 + 34X3 + 48X4 + 17X5 + 32X6 + 23X7 ? 100
Additional constraints are:
X1 + X2? 1 (#1 & #2 are mutually exclusive)
X3 + X4 ?1 (#3 & #4 are mutually exclusive)
The final constraint, "neither #3 or #4 may be selected unless either #1 or #2 are selected", may be stated thus:
X3? X1 + X2
X4 ? X1 + X2
or, since #3 and #4 are mutually exclusive, by the single constraint
X3 + X4 ?X1 + X2
The LINDO output follows:
Maximize 17X1 + 10X2 + 15X3 + 19X4 + 7X5 + 13X6 + 9X7
SUBJECT TO
43X1 + 28X2 + 34X3 + 48X4 + 17X5 + 32X6 + 23X7 ? 100
X1 + X2? 1
X3 + X4 ?1
X3? X1 + X2
X1 - X2 + X3 ? 0
-X1 - X2 + X4 ? 0
Related Questions
drjack9650@gmail.com
Navigate
Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.