**Quantitative Analysis for Decision Making Question and Answer Assignment**

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**Assignment for Quantitative Analysis for Decision Making **

**Formulate the linear programming model****solve using graphical solution Method****solve using simple method**

*1. Z=10X _{1}+15X_{2 }*

* St:
*

*2X _{1}+X_{2 }< 26*

*2X _{1}+4X_{2}< 56*

*X _{1, }X_{2 }>_{ }0*

*2. Min.Z=3X _{1}+2X_{2}*

* ** St:*

* 5X _{1}+X_{2 }> 10*

*X _{1} +X_{2 } > 6*

*X _{1 +} 4 X_{2 }> 12*

*X _{1, }X_{2 }>0*

**3. Max.Z=6X_{1}-4X_{2}**

* St:
*

*X _{1}+X_{2 }< 1*

*X _{1}+X_{2}> 3*

*X _{1 + }X_{2}>_{ }2*

*X _{1, }X_{2 }>_{ }0*

*4. Max.Z=3X _{1}+2X_{2}*

* St:*

*2X _{1}+4X_{2 }< 4*

*4X _{1}+8X_{2}> 16*

*X _{1, }X_{2 }>_{ }0*

**5. Min.Z=20X_{1}+10X_{2}**

** St:**

*St.X _{1}+2X_{2}> 40*

*3X _{1 +} 4 X_{2 }> 30*

*4X _{1}+ 3X_{2}> 60*

**6. Min Z=4 X_{1} +3X_{2}**

**20 X_{1} +10X_{2 }>230**

*X _{1} *+15

*X*

_{2 }__>__120

*X _{1},*

*X*

_{2 }__>__*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 r_{1} and r_{2 }are required for production. At least 18 Kg of **r _{1}** and 12 Kg of

**r**must be used daily. Almost at most 34 hours of labor are to be utilized .2Kg of

_{2}**r**are needed for each model

_{1}**X**and 1Kg of

**r**for each model

_{1}**Y**. For each model of

**X**and

**Y**, 1Kg of

**r**is required. It needs 3 hours to manufacture model

_{2}**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

**respectively for his garden. A liquid product contains 5, 2 and 1 units of**

*C***,**

*A***and**

*B***respectively per jar. A dry product contains 1, 2 and 4 units of**

*C***,**

*A***and**

*B***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?**

*C*

11. A car rental company has one car at each of five depots ** a, b, c, d** and

**. A customer in each of the five towns**

*e***and**

*A, B, C, D***requires a car. The distance in (in kilometers) between the depots and towns where the customers are, is given in the following distance matrix:**

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

12. Consider the following TP

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