1. Solve graphically:

Minimize Z=6x_{1} + 14x_{2}

Subject to

5x_{1} + 4x_{2} ≥ 60

3x_{1} + 7x_{2} ≤84

x_{1} + 2x_{2} ≥ 18

x_{1}, x_{2} ≥ 0

2. Using the following cost matrix, determine (a) optimal job assignment, and (b) the cost of

assignments.

Job

Mechinist | 1 | 2 | 3 | 4 | 5 |

A | 10 | 3 | 3 | 2 | 8 |

B | 9 | 7 | 8 | 2 | 7 |

C | 7 | 5 | 6 | 2 | 4 |

D | 3 | 5 | 8 | 2 | 4 |

E | 9 | 10 | 9 | 6 | 10 |

3. “In goal programming, we attempt to ‘satisfy’ or come as close as possible to satisfying, the various goals,” Discuss.

4. A wholesaler supplies 30 stuffed dolls each day to various shops. Dolls are purchased from the manufacturer in lots of 120 each at Rs. 1200 per lot. Every order incurs a handling charge of Rs 60 plus a freight charge of Rs 250 per lot. Multiple and fractional lots can also be ordered, and all orders are met the next day. The incremental cost is Rs 0.60 per year to store a doll in inventory. The wholesaler finances inventory investments by paying its holding company 2% monthly for borrowed funds.

How many dolls should be ordered at a time in order to minimize the total annual inventory cost? Assume that there are 250 week-days in a year. How frequently should he order?

5. What is simulation? Describe the simulation process. State the major two reasons for using simulation to solve a problem. What are the advantages and limitations of simulation?

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