Explanation Meaning of Introducing a new product mean introducing a new variable to the original simplex problem to maximization or minimization (and thus a new column) under the assumption that the new product was to have no effect on the optimal solution. It can become very simple by determining of duality of primal, then the solution to the dual of the original problem would still be optimal and can be used to determine the value that would need to be assigned to the new variable in the objective function to alter the solution. This can be understood as below: Consider a problem to determine the profit on the sale of each brand D that the store would gain on stereo set in order to justify to carry it. If the number of brand A type stereo system is a , brand B type stereo system is b , brand C type stereo system is c . The final tableau of the above problem is: a b c u v w M b v w M [ 1 1 1 1 0 0 0 100 1 0 0 − 4 1 0 0 80 20 0 10 − 20 0 1 0 1200 140 0 70 210 0 0 1 21 , 000 ] Where, optimal solution is b = 100 , v = 80 , w = 1200 , and M = 21000 . Now introduce third variable d which denotes the number of 4 th brand D , and price per unit of brand D stereo system is p

Finite Mathematics & Its Applications (12th Edition)

12th Edition

ISBN: 9780134437767

Author: Larry J. Goldstein, David I. Schneider, Martha J. Siegel, Steven Hair

Publisher: PEARSON

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Chapter 4, Problem 11FCCE

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How the dual problem can be used to decide whether to introduce a new product.

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Finite Mathematics & Its Applications (12th Edition)

Ch. 4.1 - 1. Determine by inspection a particular solution...Ch. 4.1 - Prob. 2CYU Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - For each of the following linear programming...Ch. 4.1 - 712For each of the linear programming problems in...Ch. 4.1 - 7–12 For each of the linear programming problems...

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How the dual problem can be used to decide whether to introduce a new product.

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