Question 1: Solve the following LP using Revised Simplex Method
2 Minimize z=2x1+x2 subject to 3x1+4x2 <= 6, 6x1+x2 <=3, x1,x2 >=0
Question 2: Solve the following transportation problem (Using VAM, Compute initial basic solution).
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|
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Destination
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Supply
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|
|
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I
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II
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III
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IV
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Source
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A
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10
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0
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20
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11
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15
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B
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12
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7
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9
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20
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25
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C
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0
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14
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16
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18
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5
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Demand
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5
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15
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15
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10
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|
Question 3 ABC Company has 4 types of jobs to be performed by 4 type of workers with varying skill and hence wages. Depending on the skill of the worker, the wages (in Rs.) per hour for four workers and four jobs are given in the following table.
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Worker/job
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J1
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J2
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J3
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J4
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W1
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5
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7
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11
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6
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W2
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8
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5
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9
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6
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W3
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4
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7
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10
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7
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W4
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10
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4
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8
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3
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Using the above tableau, find out the optimal assignment of job to each worker. Also find out the optimal cost of performing the jobs.
Question 4: The table below lists all the activities and their respective durations for a small engineering activity
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Activity
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1-2
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2-3
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2-4
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3-4
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3-5
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3-6
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4-5
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4-6
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5-6
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Duration (weeks)
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3
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3
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2
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0
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3
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2
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7
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5
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6
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For the above table:
(i) Construct the network showing all the possible paths
(ii) Find the critical path showing each activity's start and finish time.
Question 5: There are two products A and B, each product requires time in 2 production department 1 & 2. Product A requires 6 hours in department 1 and 3 hours in department 2. Product B requires 3 hours in department 1 and 6 hours in department 2. Production time is limited in department 1 to 90 hours and in department 2 to 72 hours. Contribution to the profits for the two products is Rs. 120 and Rs. 90 per unit respectively.
(i) If the total desired profit is Rs 21,000, formulate the Goal programming model for the above.
(ii) If the company sets two equally ranked goal one to achieve the profit of Rs. 15000 and the other to meet the production goal of product A as 10 units. Reformulate the goal programming model.