Formulate the linear programming model, develop a spreadsheet, and solve the capital rationing problem in Example 12.1 with an investment limit of (a) $20 million, as presented, (b) $13 million, and (c) $30 million.
What will be an ideal response?
To develop the 0-1 ILP formulation, first calculate PWE, since it was not included in Table 12-2. All amounts are in $1000 units.
PWE = -21,000 + 9500(P/A,15%,9)
= -21,000 + 9500(4.7716)
= $24,330
The linear programming formulation is:
Maximize Z = 3694x1 - 1019 x2 + 4788 x3 + 6120 x4 + 24,330 x5
Constraints: 10,000x1 + 15,000 x2 + 8000 x3 + 6000 x4 + 21,000 x5 < 20,000
xk = 0 or 1 for k = 1 to 5
(a) For b = $20 million: The spreadsheet solution uses the template in Figure 12-5. MARR is set to 15% and a constraint is set to $20,000 in Solver. Projects C and D are selected (row 19) for a $14,000 investment with Z = $10,908 (cell I2), as in Example 12.1. (Note: Set the solving method to Simplex LP)
 ANSWER.png)
(b) b = $13 million: Reset the budget constraint to b = $13,000 in Solver and obtain a new solution to select only project D with Z = $6120 and only $6000 of the $13,000 invested.
(c) b = $30 million: When the constraint is reset to $30,000, projects D and E are selected with the maximum Z = $30,450 and $27,000 invested.
You might also like to view...
Figure 12-4
The circuit shown in the accompanying figure permits ____________________ motors to start in sequence.
Fill in the blank(s) with the appropriate word(s).
Cuando se mueve una grúa móvil sin las indicaciones del maniobrista, tres señales de movimiento del avisador acústico de la grúa significan que _____.
a. la pluma se está elevando b. la grúa se está deteniendo c. la grúa está avanzando d. la grúa se está moviendo en reversa
The two immigrant ethnic groups who were most harshly treated in the mid-to-late 19th century were the
A. Spanish and Portuguese. B. Irish and Chinese. C. Germans and Italians. D. Japanese and Filipinos. E. Slavs and Russians.
Fruit trees and flowering shrubs make excellent indoor plants
Indicate whether the statement is true or false