Reference no: EM132328261
Questions -
Q1. Solve the following LP to obtain the optimal solution.
Maximize Z = 5X1 + 3X2 + 7X3
S.T. 4X1 + 3X2 + 2X3 ≤ 50
2X1 + 3X2 + X3 ≤ 30
3X1 + 2X2 - X3 ≤ 15
X1, X2, X3 ≥ 0
Q2. Solve the following LP (use Excel)
Minimize Z = 2X1 +4X2 + 3X3
S.T. X1 +4X2+ 2X3 ≥ 30
X1 + 2X2 + 2X3 ≥ 25
X1, X2, & X3 ≥ 0
Q3. Find the starting tableau for the following Transportation problem using Vogel's Method.
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D1
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D2
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D3
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D4
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D5
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Q
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S1
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6
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8
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4
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3
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9
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30
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S2
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4
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3
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5
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7
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4
|
|
20
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S3
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9
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5
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7
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4
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2
|
|
25
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S4
|
7
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4
|
6
|
9
|
5
|
|
35
|
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S5
|
8
|
7
|
10
|
5
|
4
|
|
15
|
|
|
|
|
|
|
|
|
|
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Q
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20
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30
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40
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30
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30
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|
|
Q4. Solve the following Assignment problem using the Hungarian Method.
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J1
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J2
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J3
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J4
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J5
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W1
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3
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9
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2
|
3
|
7
|
|
W2
|
6
|
3
|
5
|
8
|
6
|
|
W3
|
9
|
4
|
7
|
10
|
3
|
|
W4
|
2
|
5
|
3
|
2
|
4
|
|
W5
|
9
|
6
|
2
|
4
|
5
|
Q.5 Formulate the following problem as LP Model
A company produce 3 products a, b and c. the selling prices per unit are AED 142, AED 185 and AED 224 respectively. The maximum demand for the 3 products are 250, 140 and 60 unit per week respectively. For the manufacturing of these products four types of raw materials are required. The prices of raw materials, the raw material units needed for each product type and the corresponding available quantities per week are included in the following table:
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RM
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PM Cost
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RM per unit of Product
|
Available RM
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AED/Unit
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a
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b
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c
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Units/Week
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|
1
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10
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2
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3
|
5
|
1000
|
|
2
|
12
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3
|
2
|
4
|
1200
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|
3
|
5
|
4
|
3
|
3
|
1500
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|
4
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6
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1
|
3
|
5
|
900
|
The company's goal is to determine the quantities of each product which should be produced in order to achieve the highest profit. Define in detail the decision variables and form the objective function and all constraints of the problem.