Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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Expert Solution & Answer
Chapter 6.3, Problem 7P
a.
Explanation of Solution
New optimal solution
- Let
- For a maximization problem, the new optimal value = (old optimal value) + (Constraint i’s shadow price).
- For a minimization problem, the new optimal value = (old optimal value) – (Constraint i’s shadow price).
- Here
b.
Explanation of Solution
Optimal basis
- Let
- For a maximization problem, the new optimal value = (old optimal value) + (Constraint i’s shadow price).
- For a minimization problem, the new optimal value = (old optimal value) – (Constraint i’s shadow price)
c.
Explanation of Solution
New optimal solution
- Let
- For a maximization problem, the new optimal value = (old optimal value) + (Constraint i’s shadow price).
- For a minimization problem, the new optimal value = (old optimal value) – (Constraint i’s shadow price).
- Here
d.
Explanation of Solution
Optimal basis
- Let
- For a maximization problem, the new optimal value = (old optimal value) + (Constraint i’s shadow price).
- For a minimization problem, the new optimal value = (old optimal value) – (Constraint i’s shadow price)
e.
Explanation of Solution
New optimal solution
- Let
- For a maximization problem, the new optimal value = (old optimal value) + (Constraint i’s shadow price).
- For a minimization problem, the new optimal value = (old optimal value) – (Constraint i’s shadow price)
Expert Solution & Answer
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Students have asked these similar questions
Consider the following linear programming problem:
Min
A
+
2B
s.t.
A
+
4B
≤
21
2A
+
B
≥
7
3A
+
1.5B
≤
21
-2A
+
6B
≥
0
A, B
≥
0
Determine the amount of slack or surplus for each constraint. If required, round your answers to one decimal place.
(1)
A + 4B ≤ 21
Slack or surplus
(2)
2A + B ≥ 7
Slack or surplus
(3)
3A + 1.5B ≤ 21
Slack or surplus
(4)
-2A + 6B ≥ 0
Slack or surplus
Solve the following exercise using jupyter notebook for Python, to find the objective function, variables, constraint matrix and print the graph with the optimal solution.
A farm specializes in the production of a special cattle feed, which is a mixture of corn and soybeans. The nutritional composition of these ingredients and their costs are as follows:
- Corn contains 0.09 g of protein and 0.02 g of fiber per gram, with a cost of.$0.30 per gram.- Soybeans contain 0.60 g of protein and 0.06 g of fiber per gram, at a cost of $0.90 per gram.0.90 per gram.
The dietary needs of the specialty food require a minimum of 30% protein and a maximum of 5% fiber. The farm wishes to determine the optimum ratios of corn and soybeans to produce a feed with minimal costs while maintaining nutritional constraints and ensuring that a minimum of 800 grams of feed is used daily.
Restrictions
1. The total amount of feed should be at least 800 grams per day.2. The feed should contain at least 30% protein…
Use appropriate de Morgan’s theorem to transform the following clauses into horn clauses
¬P∧¬Q
¬(P∧Q)
3. P∧Q ∧ ¬(¬P∧¬Q)
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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