V₁ V₂ V3 Supply 5 3 1 U₁ 10 2 3 4 20 112 4 2 30 U3 Demand 15 20 25 A) Find a basic feasible solution, by using - Northwest corner method. B) Check if the initial solution is optimal if not find it, by using method of multipliers
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- 26. XYZ and Co has provided the following data seeking your advice on optimum investment strategy: Net return data (in paise) Investment made at the of selected investments Amount beginning of year available (Lakh) 1 95 80 70 60 70 2 75 65 60 50 40 3 70 45 50 40 90 60 40 40 30 30 Маximum Investment (Lakh) 40 50 60 60 The following additional information is also provided: (i) P, Q, R and S represent the selected investments. (ii) The company has decided to have four-year investment plan. (iii) The policy of the company is that amount invested in any year will remain so until the end of the fourth year. (iv) The values (paise) in the table represent net return on investment of 7 1 till the end of the planning horizon (for example, a rupee invested in investment P at the beginning of first year will grow to { 1.95 by the end of the fourth year, yielding a return of 95 paise). Using the above, determine the optimum investment strategy. (CA, November, 1996)Qn1. Find the optimal solution to the transportation problem using MODI method. Warehouses Supply WI W2 W3 W4 P1 19 30 50 12 Plants 5. 2. P2 70 30 40 60 P3 40 10 60 20 3. 15 Demand 4)Solve the following decision tree using the EMV rule and state the optimal strategy. B C .25 D 35 E 40 F 2 G 8 20 -50 H J K M N R 180 50 S 55 T 45 U 25 V 35 W S X 5 Y 4 Z 6 AA 3 BB 4 CC 3 300 100 10 80 -30 120 500 --200 150 100 50
- 8. Palmer Jam Company is a small manufacturer of several different jam products. One product is an organic jam that has no preservatives, sold to retail outlets. Susan Palmer must decide how many cases of jam to manufacture each month. The probability that demand will be 5 cases is 0.05, for 6 cases it is 0.30, for 7 cases it is 0.50, and for 8 cases it is 0.15. The cost of every case is $45, and the price Susan gets for each case is $90. Unfortunately, any cases not sold by the end of the month are of no value as a result of spoilage. Part 2 Based on the given information, Susan's conditional profits table for jam is: Demand 5 cases 6 cases 7 cases 8 cases Produce p=0.05 p=0.30 p=0.50 p=0.15 5 cases __________ ___________ ___________ ____________ b) The number of cases that Susan should produce to achieve maximum expected value (EMV) is _____ cases. c) The EMV of stocking this number of cases is $_______.9.2-6. Consider the transportation problem having the following parameter table: Plants respecti and 20 Th Destination 4 Supply mine the 1. 9. 20 30 30 20 to the re 8. 4 9. Source 7. minimiz (а) Fort 3. 6. 4(D) 0. 0. stru Demand (b) Use solu (c) Star tivel tima 25 25 10 20 After several iterations of the transportation simplex method, a BF solution is obtained that has the following basic variables, x= 20, 20. Continue the transportation simplex method for wo more iterations by hand. After two iterations, state whether the solution is optimal 25, 5, X2 =0, x – 0, 15 9.2-9. T systems The (1) electr ing. The and, if so, why. D1.9.2-7. Consider the transportation problem having the fol- 740O 20what is the shawdow price of constraint 1?
- Briefly explain these terms:a. Basic variableb. Shadow pricec. Range of feasibilityd. Range of optimality2. Consider the transportation problem having the following parameter table (M is a big positive number) Source Demand 1 12345 2 3 5 1 2 3 343800 13 14 4 18 3 0 130940 Destination 4 5 22 29 18 21 M 3 5 26M940 16 M 11 24 34 19 23 11 4 6 Supply 0 ooooo 0 6 0 0 36 28 0 5 6 2 56743 (a) Use the northwest corner rule manually to obtain a complete initial BF solution, also find the objective value for this solution. How many basic variables are there in this solution? (b) Use Vogel's approximation method manually to select the first basic variable for an initial BF solution. (Attention, do not need to find an complete initial BF solution, just find the first BV for this initial BF solution)6. Find the formulation for the coffee demand in Dubai. 7. Find the constraints will ensure that if Roaster A is selected then Roaster E cannot be selected.
- Dorothy’s pastries are freshly baked and sold at several spe-cialty shops throughout Perth. When they are a day old, theymust be sold at reduced prices. Daily demand is distributedas follows:Demand Probability50 0.25150 0.50200 0.25Each pastry sells for $1.00 and costs $0.60 to make. Each onenot sold at the end of the day can be sold the next day for$0.30 as day-old merchandise. How many pastries should bebaked each day?The village board of Park City, Utah, arranges for the clearing of all snow in city streets. Weekly snowfall during the winter is normally distributed with a mean of 10 inches and a standard deviation of 4 inches. The board is considering a long term contract with a snow removal company. The long- term contract costs $1000 per truck per week. Thus, if the board signs a long-term contract for 12 inches, they pay $12,000 per week whether the trucks are used or not. Each truck is capable of clearing 1 inch of snow per week. If snowfall in a week exceeds the quantity that can be handled by the trucks included in the long term lease, the board must make emergency arrangements at a cost of $2,500 for each additional truck brought in. For how many trucks should the board sign a long term contract?1. Explain the meaning of the expected value of perfect information (EVPI) in this problem. Based on the results of (iii) and (iv), which investment would you choose? 2. Compute the coefficient of variation, the return-to-risk ratio (RTRR) for each investment. Based on (vii) and (viii), what investment would you choose? Compare the results of (vi) and (ix) and explain any differences