MTH601 Midterm Solved Paper 2005

MTH601 Midterm Exam Solved Paper 2005 – Operations Research

SEMESTER SPRING

Total Marks = M= 50

For the following project diagram find out Earliest start time (EST), Earliest finish time (EFT), Latest start time (LST), Latest finish time (LFT) for each activity. Also find the Critical Path.

NOTE: There is no need of making diagram corresponds to each step, you have to write down only the required terms correspond to each activity and the justification for the critical path. Demand for the product is 600 units per year, and the items are withdrawn at a constant rate. The setup cost for placing an order to replenish inventory is $25. The unit cost of each item is $3, and the inventory holding cost is $0.05 per item per week.

(a). Assuming shortages are not allowed, determine how often to make a production run and what size it should be.

(b). If shortages are allowed but cost $2 per item per month, determine how often to order and what size the order should be.

Solution:

Rabbani and Sons of Sialkot manufacture sports goods like hockey sticks, cricket bats etc .Each hockey stick yields a profit of Rs.20 and each cricket bat Rs 25.A hockey stick requires four hours of processing at machine A and two hours at machine B. A bat requires six hours of processing at machine A and five hours at machine Band one hour at machine C. Machine A has a maximum of 135 hours of availability capacity, machine B has 75 hours and machine C has 20 hours.

Read the above problem carefully and formulate it as an LP model to maximize the company’s profit.