(a)Explain the conditions that guarantee you to use the big – M method or the tw
ID: 393094 • Letter: #
Question
(a)Explain the conditions that guarantee you to use the big – M method or the two phase method in solving the linear programming problem.
(b)Explain the significance of the following variables with examples:
(i)Slack variables
(ii)Surplus variables
(iii)Artificial variables
Old hens can be bought for K 2 each but young ones cost K 5 each. The old hens lay 3 eggs per week and young ones 5 eggs per week, each egg being worth 30 ngwee. A hen costs K 1 per week to feed. If a person has only K 80 to spend on the hens, how many of each kind should he buy to get a profit of more than K6 per week assuming that he cannot house more than 20 hens? Use the Big M-Method to solve the problem
Explanation / Answer
1.
Contrasting the Big M simplex strategy and the Two-Phase simplex technique, weobserve the accompanying:
The fundamental way to deal with the two strategies is the same. Both add the fake factors to get the underlying accepted framework and afterward determine them to zero as quickly as time permits.
The succession of scenes and the premise changes are indistinguishable.
The quantity of cycles are the same.
The Big M simplex technique takes care of the straight issue in one pass while the Two-Phase simplex strategy comprehends it in two phases as two direct projects.
2.
Slack Variables :
Slack variable speaks to an unused curiously of assets ; it is added to not exactly or break even with (<) to type requirements keeping in mind the end goal to get a correspondence imperative.
Surplus Variables :
A surplus variable speaks to the sum by which arrangement esteems surpass an asset. These factors are additionally called 'Negative Slack Variables' . Surplus factors like slack factors convey a zero coefficient in the goal work. it is added to more prominent than or equivalent to (>) type limitations so as to get a correspondence requirement.
Artificial Variables :
Artificial Variables are added to those limitations with fairness (=) and more noteworthy than or equivalent to ( > ) sign. An Artificial variable is added to the imperatives to get an underlying answer for a LP issue. Counterfeit factors have no importance in a physical sense and are not just utilized as a device for creating an underlying answer for a LP issue.
3.
Maximize (Z) = 0.3(3x1+5x2)-1(x1+x2)=- 0.1x1+.5x2
Subject to constraints
2x1+5x2 80,
x1+x2 20,
-0.1x1+5x26
Since, x1, x20
Z=8, x1=0, x2=16
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