Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
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Chapter 6.7, Problem 4P
Program Plan Intro
Linear
- The linear programming (LP) is also known as linear optimization.
- Consider a mathematical model, and its requirements are used to represent by the linear relationships. The linear programming is the best method to achieve the best outcome of this mathematical model. The outcomes may be, maximum profit or lower cost.
- The linear optimization is also called as mathematical optimization because, it is a special case of mathematical programming.
- More formally, the LP is a technique for optimizing linear objective function subject to constraints of linear equality and linear inequality.
Dual of LP:
The dual of the given LP is another LP derived in the following schematic way from the original (the primal) LP.
- Every variable in the primal Linear Programming becomes a constraint in the dual LP.
- Every limit in the primal Linear Programming becomes a variable in the dual LP.
- In the dual LP, the objective direction is inversed. That is, the maximum in the primal becomes minimum in the dual and vice-versa.
Explanation of Solution
Optimal solution of the dual:
The optimal solution to the dual is,
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Based on the given problem, create an algorithm and a block diagram, and write the program code:
Function: y=xsinx
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Each step in the block diagram must be clearly shown.
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Based on the given problem, create an algorithm and a block diagram, and write the program code:
Function: y=xsinx
Interval: [0,π]
Requirements:
Create a graph of the function.
Show the coordinates (x and y).
Choose your own scale and show it in the block diagram.
Create a block diagram based on the algorithm.
Write the program code in Python.
Requirements:
Each step in the block diagram must be clearly shown.
The graph of the function must be drawn and saved (in PNG format).
Write the code in a modular way (functions and the main part should be separate).
Please explain and describe the results in detail.
Based on the given problem, create an algorithm and a block diagram, and write the program code:
Function: y=xsinx
Interval: [0,π]
Requirements:
Create a graph of the function.
Show the coordinates (x and y).
Choose your own scale and show it in the block diagram.
Create a block diagram based on the algorithm.
Write the program code in Python.
Requirements:
Each step in the block diagram must be clearly shown.
The graph of the function must be drawn and saved (in PNG format).
Write the code in a modular way (functions and the main part should be separate).
Please explain and describe the results in detail.
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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