Quantitative Analysis for Decision Making Question and Answer Assignment

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Assignment for Quantitative Analysis for Decision Making        

1. Formulate the linear programming model
2. solve using graphical solution Method
3. solve using simple method

1. Z=10X₁+15X₂

     St:

2X₁+X₂ < 26

2X₁+4X₂< 56

X_1, X₂     >   0

2. Min.Z=3X₁+2X₂

    St:

 5X₁+X₂ > 10

X₁ +X₂   > 6

X_{1 +} 4 X₂  > 12

X_1,          X₂  >0

3. Max.Z=6X₁-4X₂

     St:

X₁+X₂ < 1

X₁+X₂> 3

X_{1 +} X₂>   2

X_1, X₂     >   0

4. Max.Z=3X₁+2X₂

    St:

2X₁+4X₂ < 4

4X₁+8X₂> 16

X_1, X₂     >   0

5. Min.Z=20X₁+10X₂

    St:

St.X₁+2X₂> 40

3X_{1 +} 4 X₂ > 30

4X₁+ 3X₂> 60

6. Min Z=4X₁ +3X₂

20X₁ +10X₂  >230

X₁ +15X₂    > 120

X₁,       X₂       >  0

7. Maximize Z = 5×1 + 3×2

Subject to       4×1 + 2×2 < 8

x1 >  3

                                  x2 >  7

Where x1, x2  0

8. Maximize Z = 5×1 + 3×2

Subject to       3×1 + 5×2  15

5×1 + 2×2  10

Where x1, x2  0

9. A manufacturer produces two different models; X and Y, of the same product .The raw materials r₁ and r₂ are required for production. At least 18 Kg of r₁ and 12 Kg of r₂ must be used daily. Almost at most 34 hours of labor are to be utilized .2Kg of r₁ are needed for each model X and 1Kg of r₁ for each model Y. For each model of X and Y, 1Kg of r₂ is required. It needs 3 hours to manufacture model X and 2 hours to manufacture model Y. The profit realized is $50 per unit from model X and $30 per unit from model Y. How many units of each model should be produced to maximize the profit?

10. A person requires 10, 12 and 12 units of chemicals A, B and C respectively for his garden. A liquid product contains 5, 2 and 1 units of A, B and C respectively per jar. A dry product contains 1, 2 and 4 units of A, B and C per carton. If the liquid product sells for $3 per jar and the dry product sells $2 per carton, how many of each should be purchased in order to minimize cost and meet the requirement?

11. A car rental company has one car at each of five depots a, b, c, d and e. A customer in each of the five towns A, B, C, D and E requires a car. The distance in (in kilometers) between the depots and towns where the customers are, is given in the following distance matrix:

1. How should the cars be assigned to the customers so as to minimize the distance traveled? Using Hungarian Method.
2. What the total cost of the optimum assignment

12. Consider the following TP

1. Obtain the basic feasible solution using NWCM and LCM
2. Obtain the optimal solution of the NWCM using either steeping stone or MODI Method
3. What is the optimal shipping cost?