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This document contains two optimization problems: 1) A linear programming problem with 4 constraints and 2 variables to minimize a objective function. 2) A transportation problem with 3 supply locations, 3 demand locations, and a cost matrix to minimize total transportation cost using the northwest corner rule. It also asks to check for degeneracy.
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- 1. bSubject to, 2X1 + 3X2 ≥ 1200 X1 + X2 ≤ 400 2X1 + 1.5X2 ≥ 900 X1, njjkjX2 ≥ 0CC OR Find out the dual form of the foxcassdfsdllowing primal problem. 9adswd Min Z = 5 X1 + 7X2 + 9 X3 Subjected toZFFsfefgFGHGHjjjFFXCZXZXCCXDF X1+X2+X3 = 20XCE X1+3X2+5X3 ≥ 60 5X2 - X3 ≤ 10 X3 ≥ 4 X1, X2,X3 ≥ 0 7. Three jobs A, B and C are to be assigned to three machines X, Y Z. The processing costs are as given in the matrix shown below. Find the allocation which will minimize the overall processing cost.Use Hungarian approach. Machines Jobs X Y Z A 19 28 31 B 11 17 16 C 12 15 13 OR There are 3 plants which supply the following quantity of coal P1= 50 kg, P2=40 kg, P3= 60 kg. There are 3 consumers who require the coal as follows C1= 20 kg, C2= 95 kg, C3= 35 kg. The cost matrix in Rs. / kg is given in the matrix. Find the schedule of transportation policy using north-west corner rule which minimizes the total transportation cost.Also check for degeneracy. 6 4 1 3 8 7 4 4 2 Group C Long answer type questions 15x1=15 8. a) Explain the basic elements of the 1st model of Queuing theory. Also write the significance of all its elements. b) A TV repairman finds that the time spent on his jobs has an exponential distribution with a mean of 30 minutes. If he repairs sets in the order in which the come in, and if the arrival of the sets follows a Poisson distribution with an average rate of 10 sets per 8 hours day, what is the expected idle of the repairman per day. How many sets are ahead of the average sets just brought in? 6+9