Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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Expert Solution & Answer
Chapter 6.4, Problem 9P
Explanation of Solution
Optimal solution of the diet problem:
- The LINDO output is considered for the Dakota problem:
- max 60DSK+30TBLS+20CHRS
- Subject to constraint
- End
- LP optimum is found at step 2
- Objective function value: 90.000000
| Variable | Value | Reduced cost |
| DSK | 2.000000 | 0.000000 |
| TBLS | 0.000000 | 5.000000 |
| CHRS | 8.000000 | 0.000000 |
| Row | Slack or Surplus | Dual prices |
| 2 | 24.000000 | 0.000000 |
| 3 | 0.000000 | 10.000000 |
| 4 | 0.000000 | 10.000000 |
- Number of iterations= 2
- The ranges in which the basis is unchanged:
| Variable | Current coefficient | OBJ coefficient ranges allowable increase | Allowable decrease |
| DSK | 60.000000 | 20.000000 | 4.000000 |
| TBLS | 30.000000 | 5.000000 | Infinity |
| CHRS | 20.000000 | 2.500000 | 5.000000 |
| Row | Current RHS | Right-hand side ranges allowable increase | Allowable decrease |
| 2 | 48.000000 | Infinity | 24.000000 |
| 3 | 20.000000 | 4.000000 | 4.000000 |
| 4 | 8.000000 | 2.000000 | 1.333333 |
- As brownies and pineapple cheesecake have no zero reduced costs, so case 2 is applied to the states where,
- “At least one of the constraints whose right hand side is being modified is a binding constraint (that is, has zero slack zero excess)”.
- In case 2 for each constraint j the ratio rj is defined as follows:
- If
- If
- If
- Here,
- The 100% rule for objective function states that,
- “If
- Also,
- “If
- “If
- Now, the lumber constraint is increased to 40 board ft and finishing hour constraint is increased to 21 hours and carpentry hour constraint in increased to 8.5 hours
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Chapter 6 Solutions
Operations Research : Applications and Algorithms
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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