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Q9 a). Solve the following LP problem using simplex method. Maximize Z = 3x1 + 2x2 + 5x3 Subject to X1 + 2x2 + X3 < 430 3 X1 + 2x3 < 460 X1 + 4x2 < 420 x1, X2, X3 > 0 b). Solve by simplex method: Max Z = 3x1 + 5x2 + 4x3 Subject to 2x1+3x28 2x2+5x310 3x1 + 2x2+4x3 <15 x1,x2,x3>0 Q 12 A). An automobile dealer wishes to put four repairmen to four different jobs. The repairmen have somewhat different kinds of skills and they exhibit different levels of efficiency from one job to another. The dealer has estimated the number of man-hours that would be required for each job-man combination. This is given in the matrix form. Find the optimum assignment that will result in minimum man-hours needed. A B C D 1 5 3 2 8 2 7 9 2 6 3 6 4 5 7 4 5 7 7 8 B). A manufacturer of bags makes three types of bags P. Q and R which are processed on three machines M1, M2 and M3. Bag P requires 2 hours on machine M1 and 3 hours on machine M2 and 2 hours on machine M3. Bag Q requires 3 hours on machine M1, 2 hours on machine M2 and 2 hours on machine M3 and Bag R requires 5 hours on machine M2 and 4 hours on machine M3. There are 8 hours of time per day available on machine M1, 10 hours of time per day available on machine M2 and 15 hours of time per day available on machine M3. The profit gained from bag P is Rs 3.00 per unit. from bag Q is Rs 5.00 per unit and from bag R is Rs 4.00 per unit. What should be the daily production of each type of bag so that the products yield the maximum profit?

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