MOI UNIVERSITY //BBM 351/ECF 31 1: OPERATIONS RESEARCH/CONTINUOUS ASSESMENT TEST INSTRUCTIONS: Answer all the questions TIME: 2Hours. 1) Describe five major phases of an operation research project in a quantitative study. (5marks) 2) The Royal Wedgetown Pottery Company has orders to be completed next week for three of its products - mugs, cups, and bowls as given in the table below. Product Mugs Order (units) (10marks) Cups 4,000 Bowls 2,400 1,000 There are three machines available for the manufacturing operations and all three can produce each of the products at the same production rate. However, the unit costs of these products vary depending upon the machine used. The unit cost in pounds (E) of each machine are given in the following table; Product Mugs Cups Bowl Machine 1.20 B 1.30 1.10 1.40 1.30 1.50 1.10 1.00 1.30 In addition, it is known that capacity for next week for machines B and C is 3,000 units and for machine A is 2,000 units. Determine the optimum solution using the Vogel Approximation Method (VAM) and the minimum cost. 3) Eyebrow cosmetics company has one beauty parlor in Nairobi. The parlor distributes two eyeshades, thus last minute and outdoor girl. The accounting department of the firm has computed the unit contribution of each eyeshade. The last minute's unit contribution is kshs.50, while that of the outdoor girl is Kshs. 60. The parlor has the receiving and packaging sections where each eyeshade must pass through them. The time requirement for each eyeshade and total time available in each section are given in the following table. Minutes required. Section Last minute Outdoor girl Minutes available (Hours Receiving 6 3000 Packaging 3000 Each month, 400 units of each eyeshade is demanded. a) Formulate a linear programming model in a standard manner. (2marks) b) Using graphical approach, determine the optimal solution. (5marks) c) Determine the shadow prices by dual formulation method and interpret it. (3marks) 4) The arrival rate of customers at the single window-booking counter of a two-wheeler agency follows a Poisson distribution and the service time follows exponential distribution and hence, the service rate also follows a Poisson distribution. The arrival rate and the service rate are 25 customers per hour and 35 customers per hour, respectively. Determine the followings; a) Utilization of the booking clerk. (2marks) b) Average number of waiting customers in the queue. (2marks) C) Average number of waiting customers in the system. (2marks) d) Average waiting time per customer in the queue. (2marks) ) Average waiting time per customer in the system. (2marks) 5) ABZ Company is in the business of training people to be computer literate. It trains people in four computer areas; programming, computer applications, networking and graphics. Trainees are charged on an hourly basis. Profit matrix showing days' expected profit in S. Compart Trainees programming Computer networking Graphics applications Kirit 8 Talesu Sukari Simba Assign the four trainees to the four computer areas to maximize the day's expected profit and the maximum profit itself. (10marks) 6)The research department of M/s Hindustan lever has recommended to the marketing department to launch a shampoo of three different types. The marketing manager has to decide one of the types of shampoo to be launched under the followings estimated payoffs for various levels of sales; Type of shampoo Estimated levels of sales 15,000units 10,000units 5,000units 30 10 10 Egg shampoo 40 15 Clinic shampoo Deluxe shampoo 55 20 What will be the marketing manager's decision if maximin, maximaxi, equally likely decision and minimax regret (10marks) criterion is applied. END