ON TWO(15 MARKS). a) A department store wishes to purchase the following quantities of ladies dress Dress type A B Quantity 150 100 75 250 more than the quantities below, (all types of dresses combined). The tenders are submitted by three different manufacturers who undertake to supply not Manufacturer Total quantity W 350 X 250 Y 150 matrix below. The store estimates that its profit per dress will vary with the manufacturer as shown in the 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 the maximum profit. Determine the initial basic feasible solution using the Vogel Approximation method(VAM) and (marks) research. b) Outline the main distinctions between the following concepts as used in operation Pure strategy and mixed strategy i) ii) iii) Feasible region and feasible solution. Basic variable and non - basic variable. (2marks) (2marks) Qmark QUESTION THRE ON TWO(15 MARKS). a) A department store wishes to purchase the following quantities of ladies' dresses Dress type A B Quantity 150 100 75 250 more than the quantities below, (all types of dresses combined). The tenders are submitted by three different manufacturers who undertake to supply not Manufacturer Total quantity W 350 X 250 Y 150 matrix below. The store estimates that its profit per dress will vary with the manufacturer as shown in the 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 Determine the initial basic feasible solution using the Vogel Approximation method(VAM) and the maximum profit. (9marks). b) Outline the main distinctions between the following concepts as used in operation research. i) ii) iii) QUESTION Pure strategy and mixed strategy Feasible region and feasible solution. Basic variable and non - basic variable. (2marks) (2marks) YION TWO( 15 MARKS), a) A department store wishes to purchase the following quantities of ladies dresses Dress type A B Quantity 150 100 75 250 more than the quantities below, (all types of dresses combined). The tenders are submitted by three different manufacturers who undertake to supply not Manufacturer Total quantity W 350 X 250 Y 150 matrix below. The store estimates that its profit per dress will vary with the manufacturer as shown in the 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 Determine the initial basic feasible solution using the Vogel Approximation method(VAM) and the maximum profit. (9marks) research. b) Outline the main distinctions between the following concepts as used in operation i) ii) iii) Pure strategy and mixed strategy Feasible region and feasible solution. Basic variable and non - basic variable. (2marks) (2marks) SESTION TWO(15 MARKS). a) A department store wishes to purchase the following quantities of ladies' dresses Dress type A B C Quantity 150 100 75 250 more than the quantities below, (all types of dresses combined). The tenders are submitted by three different manufacturers who undertake to supply not Manufacturer Total quantity W 350 X 250 Y 150 matrix below. The store estimates that its profit per dress will vary with the manufacturer as shown in the 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 the maximum profit. Determine the initial basic feasible solution using the Vogel Approximation method(VAM) and (9marks). b) Outline the main distinctions between the following concepts is used in operation research. i) ii) iii) Pure strategy and mixed strategy Feasible region and feasible solution. Basic variable and non - basic variable. (2marks) (marks) 200 Approximation method VAM) and Omartia Ween the following concepts as used in operation egy and mixed strategy Casible region and feasible solution. Basic variable and non-basic variable. 2marks) Chmarks Cmarks QUESTION THREE (15 MARKS). operation on various products is given as follows; Three machine shops A, B and C produces three types of products X, Y, and Z respectively Each product involves operation of each of the machine shops. The time required for each Products X Y Z Machine shops A B C 10 7 2 2 3 1 2 per unit of products X, Y and Z is $12, $3 and $1 respectively. The available hours at the machine shops A, B and Care 100, 77 and 80 respective Depre it. g model in a standard manner. (4marks) Uphate technique, determine an optimal solution and the maximum c) Evaluate the shadow prices and give its interpretations. (8marks) (3marks) QUESTION FOUR (15 MARKS). a) 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 distriution 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; i) Average number of waiting customers in the queue. ii) Average number of waiting customers in the system. iii) Average waiting time per customer in the queue. iv) Average waiting time per customer in the system. (2marks) (2marks) (2marks) (2marks). b) i) In an inventory model, the total cost is the sum of the fixed cost and variable cost. The fixed cost is independent of order size while the variable cost is dependent on the order size. Therefore, the total cost is given as; TC = CD + Co + Ch; where TC is the total cost, Q is the order size, CD is the fixed cost, Co is ordering cost, Ch is the holding cost or carrying cost per unit of item per one year time period. It is expressed either in terms of cost per unit per period or in terms of percentage charge of the purchase price. D is deterministic demand in units per year, and Q/2 is the average inventory per cycle, since the safety stock (buffer stock) is not need, hence it is zero. Show that the order size or economic order quantity is given as; (3marks) e year time S of percentage charge Jar, and Q/2 is the average Mock) is not need, hence it is zero. Show that lly is given as; Ch (3marks) the optimal order size and number of orders per year. ii) A manufacturer uses $20,000 worth of an item during the year. The manufacturer estimated the ordering cost as $50 per order and holding costs as 12.5% of average inventory value. Find QUESTION FIVE (15 MARKS). a) You are given below the preceding activities and activity duration in days. Preceding activity Duration(days) 9 (4marks) Activity A B C - -O A 3 8 BBM 351/ECF 311 88 6 16 12 8. 5 9 13 13 12 11 7 13 20 10 QUESTION SIX (15 MARKS). a) Players A and B play a game in which each player has three coins, thus 20P, 25P and 50P. Each of them selects a coin without the knowledge of the other person. If the sum of the values of the coins is an even number, A wins B's coin. If that sum is an odd number, B wins A's coin. Determine a payoff matrix with respect to player A and the optimal strategies for the players. (7marks) b) Dr. Thomas has been thinking about starting his own independent nursing home. The problem is to decide how large the nursing home should be. The annual returns will careful analysis, Dr. Thomas developed the following table; depend on both the size of nursing home and a number of marketing factors. After a BBM 351/ECF 311 Small Size of nursing home Good market () Fair Market () 50,000 20,000 Poor market () -10,000 Medium 70,000 35,000 -25,000 ery large termine, 90,000 35.000 200,000 25.000 45.000 -120,000 i) The maximin decision. The equally likely decision. (2marks) (2marks) ) The criterion of realism decision where a = 0.8 (2marks) The minimax decision. (2marks) ** * * * **** *******E_N_D********