lp8- practice problems
TRANSCRIPT
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8/18/2019 Lp8- Practice Problems
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LP-SIMPLEX PRACT ICE PROBLEMS
Q1) Maximize z = 3x1 + 4x2 + 2x3
Subject to
X1 – 2x2 + 4x3 = 0
Q5)
Maximize Z= − +
Subject to
2 + +3 ≤ 7
2 − +4 ≥ 8
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, , ≥ 0
Solve using artificial variables Use both BIG M method and TWO PHASE method.
Q6). Solve the following LP
Minimize Z = X1 + 3X2 + X3
Subject to
X1 + X3>=30
X2 + 2X3>=40
a) Using the Two Phase Method
b) Also, find the dual of this LP and its solution
Q7) Maximize f = 200x1 + 400x2
ST: t: x1/40 + x2/60 0
a)
Write the dual to the following problem and verify that (2,0) is a feasible solution to
the dual
b) Use the information in part (a) to obtain the optimal solutions to primal and dual.
Q9)
Maximize Z= 8 +4 +9
Subject to
7 +6 + ≤ 20
4 +3 +2 ≤ 29, ≥0
Solve dual optimally
Q10)
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A factory manufactures three products. Two resources- material and labour are
required to produce these products as shown below.
Product Resources(hours) Units
Profit(Rs.)Material Labour
1 1 5 9
2 1 2 73 1 3 5
There are 80 units f material and 250 hours of manpower available. In order to determine
the optimal product mix which maximizes the total profit, the following linear program
was solved.
Maximize 9 +7 +5
Subject to
+ + ≤ 80
5 +2 +3 ≤ 250
, , >0
The optimal solution is shown in the table below.
4 -3 3 0 0
Basis b
X2
1
1
0
0
1/3
2/3
-2/3
5/3
1/3
-1/3
30
50
− 0 0 -8/3 -20/6 -4/6 Z=620
Using sensitivity analysis, answer the following with respect to above table:
(a) What should be the profit of product 3 before it becomes worthwhile to manufacture?
Find the most profitable product mix if the profit on product 3 was increased to Rs.8.
(b) What is the range of profit of Product 1 so that the current solution is still optimum.
(c) It is believed that the estimate of the available hours of labour is 250+. find the
range of values of for which the given product mix is still optimal.