MTH601 Midterm Past Paper 2004

MTH601 Operations Research · Mid Term Examination - November 2004 · Time Allowed: 90 Minutes · Instructions

3. In Q3 you can either draw the network diagram or simply write the asked terms for each activity in the exam software, whichever you think is easy for you. But remember that you have to show your work on exam application correspond to each question.

Total Questions: 3

Q1. Marks : 10

A small plant makes two types of automobile parts Part A and Part B. It buys castings that are machined, bored and polished. You are given the following data. Castings for Part A cost Rs. 20/- each and for Part B they cost Rs. 30/- each. They sell for Rs. 50/- and Rs.60/- respectively. The three machines have running costs of Rs. 200/-, Rs.140/- and Rs. 175/- per hour. Assuming that any combination of Part A and B can be sold. Formulate a linear programming model.

Or

Solve the following problem using simplex method:

Maximize Z = 9x1 + 8x2 + 7x3 Subject to

x · x · x · x · x · x · x · x · x · x · x · x

Q2. Marks : 10

Consider the following Network, figures in the boxes are the durations. Determine (a) The earliest expected completion time for each period, (b) The latest allowable event completion time for each event (c) The slack time (all floats) for each event (d) The Critical Path through the Network

Q3. Marks : 10

The demand for a purchased item is 2000 units per month and the shortages are allowed. If the unit cost is Rs 20 per unit, the cost of making one purchase is Rs 1000, the holding cost for 1 unit is Rs 20 per year and the cost of one shortage is Rs 500 per year, determine: (a) The economic purchase quantity. (b) The time between orders. (c) The number of orders per year. (d) The optimum shortages. (e) The maximum inventory. (f) The time of items being held. (g) The optimum annual cost.

Or

A company produces 36000 units per year and the demand of the product is 2400 items per year. The unit cost is Rs 10 per item, the holding cost is one rupee per month per item and the set up cost is Rs 100, determine the following if no shortages are allowed (a) Optimum manufacture quantity (b) The maximum inventory (c) The time between setups (d) The number of setups (e) The manufacturing time (f) The total optimum annual cost