a). Solve the following LP problem using simplex method.
Maximize Z = 3x1 + 2x2 + 5x3
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
3x1 + 2x2+4x3 <15
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.
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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