A farmer is raising pigs for market and wishes to determine the quantities of the available types of feed that should be given to each pig to meet certain nutritional requirements at a minimum cost. The numbers of each type of basic nutritional ingredient contained within a kilogram(kg) of each feed type is given in the following table along with the daily nutritional requirements and the feed costs: (15marks) Nutrients Corn Tankage Alfalfa Minimum requirement. Carbohydrates 9 1 4 20 Protein 3 8 6 18 Vitamins 1 2 6 15 Costs (in kshs) 7 6 5 What is the best solution to the farmer? Bi Near re wParagraph Styles counterfeiting. Avoid interruption and keep your files safe with genuine Office today. Get genuine Office 4 . . . 1 5 Consider the following activities, associated normal time and cost, together with the extra cost of saving a day on selected activities. Activity Normal cost of Normal time in days Extra cost of activity (f) reducing normal time by one day (E) A to B 10,000 5 3,000 A to C 12,000 7 2,000 A to D 5,000 9 800 B to C 6,000 10 600 B to E 9,000 8 2,000 B to F 5,000 6 900 C to D 4,000 4 700 C to F 3,000 3 200 D to F 5,000 7 2,000 E to F 6,000 12 500 No single activity can be reduced by more than one day. In addition, site costs will be incurred at the rate of $3,500 for every day that work is in progress on the site irrespective of how many activities are in progress. Determine and state, (10marks) a) The network diagram, critical path, using normal time, the time taken and the total cost of completing the project. b) The shortest time in which the project can be completed, the associated cost and the critical path. c) The lowest cost for which the project can be completed and the associated cost and time. (Ctrl) * W SunAaBbCcDd AaBbCcDd AaBbCc AaBbCct Aa B AaBbCc Normal No Spac.. Heading 1 Heading 2 Title Subtitle Paragraph Styles counterfeiting. Avoid interruption and keep your files safe with genuine Office today. Get genuine Office 1 . . A and B play a game as follows: They simultaneously and independently write one of the three numbers 1, 2, 3. If the sum of the numbers written is even, Player B pays player A this sum in pounds. If it is odd, player A pays the sum to B in pounds. Develop a pay - off matrix with respect to player A and find the optimal strategies for the players. 21 C Mostly wAaBbCcDd AaBbCcDd AaBbCc AaBbCct Ad B AaBbCCD AaBbCcDd E Normal No Spac... Heading 1 Heading 2 Title Subtitle Subtle Em... Paragraph Styles software counterfeiting. Avoid interruption and keep your files safe with genuine Office today. Get genuine Office Learn more A 2 7 1) A department store wishes to purchase the following quantities of ladies' dresses. Dress type A B C D Quantity 150 100 75 250 I The tenders are submitted by three different manufacturers who undertake to supply not more than the quantities below, (all types of dresses combined). Manufacturer W X Y Total quantity 350 250 150 The store estimates that its profit per dress will vary with the manufacturer as shown in the matrix below. Manufacturer Dress A B C D W 2.75 3.50 4.25 2.25 X 3.00 3.25 4.50 1.75 Y 2.50 3.50 4.75 2.00 a) Determine the initial basic feasible solution using the Northwest corner method and the maximum profit. (5marks) b) Evaluate each unused cells by the modified distribution (MODI) method and showing improvements in indices, determine the maximum profit. (10marks) w 21'C Mostly sunnyDocument7 [Compatibility Mode] - Word W View Help Tell me what you want to do AJ IT AaBbCcDd AaBbCcDd AaBbCc AaBbCct Aa B AaBbC Normal No Spac... Heading 1 ng 2 Title Subtitl Paragraph 15 Styles counterfeiting. Avoid interruption and keep your files safe with genuine Office today. Get genuine Office 5 . 6 . . . In a market research survey on use of bathing soaps, the findings were as follows; Out of those who used lux at last purchase, 10% switched to Jai, 10% switched to Liril, and 10% switched to Hamam. Out of those who used Jai, 20% switched to Liril, and 10% to Hamam. Out of those who were using Liril, only 10% switched to Hamam. Out of those who used Hamam, 20% switched to Lux, 10% to Jai, and 10% to Liril. Assuming that the bathing soaps' switching patterns continue, determine; a) A transition probability Matrix. b) The long - run Market shares. (10marks). 21'C MostMOI 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