OPERATIONS RESEARCH >INTERNATIONAL EDITI
4th Edition
ISBN: 9780534423629
Author: WINSTON
Publisher: CENGAGE L
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Chapter 6, Problem 37RP
Program Plan Intro
Optimal solution:
- Here, consider the LP:
- min z=
- Subject to constraints:
- Where
- In order to calculate the optimal solution of the primal, use the software Lindo
- Step 1:
- Type in the Linear Program in the command window. Select yes when asked about the range analysis.
- The output is shown below:
- LP optimum found at step 7
- Objective function value: 78450
| Variable | Value | Reduced Cost |
| 40.000000 | 0.000000 | |
| 40.000000 | 0.000000 | |
| 40.000000 | 0.000000 | |
| 25.000000 | 0.000000 | |
| 0.000000 | 20.000000 | |
| 10.000000 | 0.000000 | |
| 35.000000 | 0.000000 | |
| 0.000000 | 50.000000 | |
| 10.000000 | 0.000000 | |
| 0.000000 | 20.000000 | |
| 0.000000 | 70.000000 | |
| 0.000000 | 420.000000 |
| Row | Slack or Surplus | Dual prices |
| 2 | 0.000000 | 30.000000 |
| 3 | 0.000000 | 50.000000 |
| 4 | 0.000000 | 50.000000 |
| 5 | 15.000000 | 0.000000 |
| 6 | 0.000000 | -430.000000 |
| 7 | 0.000000 | -450.000000 |
| 8 | 0.000000 | -450.000000 |
| 9 | 0.000000 | -400.000000 |
- Number of iterations=7
- Ranges in which the basis is unchanged:
| Obj coefficient ranges | |||
| Variable | Current coefficient | Allowable increase | Allowable decrease |
| 400.000000 | 30.000000 | Infinity | |
| 400.000000 | 50.000000 | Infinity | |
| 400.000000 | 50.000000 | Infinity | |
| 400.000000 | 50.000000 | 400.000000 | |
| 450.000000 | Infinity | 20.000000 | |
| 450.000000 | 20.000000 | 20.000000 | |
| 450.000000 | 20.000000 | 50.000000 | |
| 450.000000 | Infinity | 50.000000 | |
| 20.000000 | 30.000000 | 20.000000 | |
| 20.000000 | Infinity | 20.000000 | |
| 20.000000 | Infinity | 70.000000 | |
| 20.000000 | Infinity | 420.000000 | |
| Righthand side ranges | |||
| Row | Current RHS | Allowable increase | Allowable decrease |
| 2 | 40.000000 | 10.000000 | 10.000000 |
| 3 | 40.000000 | 10.000000 | 40.000000 |
| 4 | 40.000000 | 35.000000 | 40.000000 |
| 5 | 40.000000 | Infinity | 15.000000 |
| 6 | 30.000000 | 10.000000 | 10.000000 |
| 7 | 60.000000 | Infinity | 10.000000 |
| 8 | 75.000000 | Infinity | 35.000000 |
| 9 | 25.000000 | 15.000000 | 25.000000 |
- Therefore, the optimal solution of primal is given by
Explanation of Solution
b.
- It can be seen from the Lindo output that the Obj coefficient ranges block is used to determine the amount by which each variable’s objective function coefficient may change before the current basis becomes suboptimal.
- If the objective function coefficient for
- Since,
- The new optimal z-value can be obtained by substituting the substituting the optimal values of the decision variables
Explanation of Solution
c.
- If the demand of the sailboat increases by 1 unit in the first quarter, then the cost would increase by $430.
- As it can be observed from row (6) Dual prices section of the Lindo output.
- Since, the amount offered is less than the rise in the total cost, there is no incentive for Sailco to cater to this new demand...
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Chapter 6 Solutions
OPERATIONS RESEARCH >INTERNATIONAL EDITI
Ch. 6.1 - Prob. 1PCh. 6.1 - Prob. 2PCh. 6.1 - Prob. 3PCh. 6.1 - Prob. 4PCh. 6.1 - Prob. 5PCh. 6.2 - Prob. 1PCh. 6.2 - Prob. 2PCh. 6.3 - Prob. 1PCh. 6.3 - Prob. 2PCh. 6.3 - Prob. 3P
Ch. 6.3 - Prob. 4PCh. 6.3 - Prob. 5PCh. 6.3 - Prob. 6PCh. 6.3 - Prob. 7PCh. 6.3 - Prob. 8PCh. 6.3 - Prob. 9PCh. 6.4 - Prob. 1PCh. 6.4 - Prob. 2PCh. 6.4 - Prob. 3PCh. 6.4 - Prob. 4PCh. 6.4 - Prob. 5PCh. 6.4 - Prob. 6PCh. 6.4 - Prob. 7PCh. 6.4 - Prob. 8PCh. 6.4 - Prob. 9PCh. 6.4 - Prob. 10PCh. 6.4 - Prob. 11PCh. 6.4 - Prob. 12PCh. 6.4 - Prob. 13PCh. 6.5 - Prob. 1PCh. 6.5 -
Find the duals of the following LPs:
Ch. 6.5 - Prob. 3PCh. 6.5 - Prob. 4PCh. 6.5 - Prob. 5PCh. 6.5 - Prob. 6PCh. 6.6 - Prob. 1PCh. 6.6 - Prob. 2PCh. 6.7 - Prob. 1PCh. 6.7 - Prob. 2PCh. 6.7 - Prob. 3PCh. 6.7 - Prob. 4PCh. 6.7 - Prob. 5PCh. 6.7 - Prob. 6PCh. 6.7 - Prob. 7PCh. 6.7 - Prob. 8PCh. 6.7 - Prob. 9PCh. 6.8 - Prob. 1PCh. 6.8 - Prob. 2PCh. 6.8 - Prob. 3PCh. 6.8 - Prob. 4PCh. 6.8 - Prob. 5PCh. 6.8 - Prob. 6PCh. 6.8 - Prob. 8PCh. 6.8 - Prob. 9PCh. 6.8 - Prob. 10PCh. 6.8 - Prob. 11PCh. 6.9 - Prob. 1PCh. 6.9 - Prob. 2PCh. 6.9 - Prob. 3PCh. 6.10 - Prob. 1PCh. 6.10 - Prob. 2PCh. 6.10 - Prob. 3PCh. 6.11 - Prob. 1PCh. 6.11 - Prob. 3PCh. 6.11 - Prob. 4PCh. 6.12 - Prob. 5PCh. 6.12 - Prob. 6PCh. 6.12 - Prob. 7PCh. 6 - Prob. 1RPCh. 6 - Prob. 2RPCh. 6 - Prob. 3RPCh. 6 - Prob. 4RPCh. 6 - Prob. 5RPCh. 6 - Prob. 6RPCh. 6 - Prob. 7RPCh. 6 - Prob. 8RPCh. 6 - Prob. 9RPCh. 6 - Prob. 10RPCh. 6 - Prob. 11RPCh. 6 - Prob. 13RPCh. 6 - Prob. 14RPCh. 6 - Prob. 15RPCh. 6 - Prob. 17RPCh. 6 - Prob. 18RPCh. 6 - Prob. 19RPCh. 6 - Prob. 20RPCh. 6 - Prob. 21RPCh. 6 - Prob. 22RPCh. 6 - Prob. 25RPCh. 6 - Prob. 29RPCh. 6 - Prob. 33RPCh. 6 - Prob. 34RPCh. 6 - Prob. 35RPCh. 6 - Prob. 36RPCh. 6 - Prob. 37RP
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