QUESTION 1
(a) Briefly outline the special cases and difficulties in Linear Programming (LP) when using the graphical method with relevant graph sketches
(b) A manufacturer produces two types of cotton cloth: Denim and Corduroy. Corduroy is a heavier grade cotton cloth and, as such, requires 3.5 kg of raw cotton per meter whereas Denim requires 2.5 kg of raw cotton per meter. A meter of Corduroy requires 3.2 hours of processing time, and a meter of Denim requires 3 hours. Although the demand for Denim is practically unlimited, the maximum demand for Corduroy is 510 meters per month. The manufacturer has 3,250 kg of cotton and 3,000 hours of processing time available each month. The production costs per meter of Denim and Corduroy are Rs 5.50 and Rs 7.00 respectively. Each meter of Denin sells for Rs 10 while each meter of Corduroy sells for Rs 13. The manufacturer is interested in finding the optimal combination of Denin and Corduroy that he should produce
(i) Formulate the complete linear programming model for the above problem. You should provide a clear definition of the components of the model
(ii) Graph the constraints lines for this linear programming problem and indicate clearly the feasible region, R
(iii) Determine the feasible corner point (X) and the quantity (in meters) of each type of cloth that the manufacturer should produce so as to maximize his profits
(c) List the limitations of Linear programming
QUESTION 2
(a) Explain three benefits of inventory control
(b) Define what is meant by the optimal ordering quantity
(c) Explain three major limitations of the basic EOQ model
(d) A catering company supplies 2000 packs of bottled water every month
The cost of placing an order with a bottling company is Rs 200. The monthly inventory holding costs are estimated to be Rs 20 per pack. A shortage fee of Rs 40 per pack per month is incurred each time the company is unable to meet a scheduled demand. Calculate-
(i) the economic order quantity?
(ii) the optimal level of inventory?
(iii) the time between orders
(iv) the re-order level
(v) the total optimal inventory cost