MARKS: 75                                                                                                                          TIME: 2.5 HR

NOTE:  Attempt All Question.

Q.1Transportation unit cost matrix –

   D1 D2 D3 D4 Capacity
P1 100 120 90 60 700
P2 70 30 70 70 600
P3 60 60 90 110 900
Demand 600 400 600 200

 Find Initial Feasible solution by VAM & Optimal solution by Modified Distribution method. Is there an alternate optimal solution? Comment.                                                                                                               10

  1. Explain Degeneracy concept in details 5

Q.2A]Explain Uses of slacks and floats in PERT and CPM                                               5

B]            For the following project, draw PERT network and find expected project completion time.


  Activity Preceding Optimistic time Most likely time Pessimistic time  
    Activity (a) in weeks (m) in weeks (b) in weeks  
  A 2 4 12  
  B 10 12 26  
  C A 8 9 10  
  D A 10 15 20  
  E A 7 7.5 11  
  F B, C 9 9 9  
  G D 3 3.5 7  
  H E, F, G 5 5 5  
Answer the following questions.      
(a) Find probability of project completion in 32 weeks.    
(b) Find probability of project completion in 27 weeks.    
(c) Find project completion time for 95% probability.    
(d) Find probability of not completing project in 30 weeks.                              10

Q.3. A ] Explain Iso-profit line in graphical solution in LPP                                                            5

B]Padma Ltd makes 3 different types of boats. All boats can be made profitably in this company but the company’s monthly production is constrained by the limited amount of labour, wood and screws available each month. The director will choose the combination of boats that maximizes his revenue, in the view of the information given in the following table.                                                    10

Input Row boat Canoe Kayak Monthly availability
Labour (hrs) 12 7 9 1260 hrs
Wood (board feet) 22 18 16 19008 board feet
Screws (kg) 2 4 3 396 kg
Selling price (`) 4000 2000 5000

   Formulate and solve by graphically.                                                                                                    10

Q.4A chemical company M/s A Industries has invented a new drug which needs to be processed and developed further. A multinational has approached Apex to sell the rights of the new drug to it. It has offered Rs. 5 million for the rights of the undeveloped drug.

Apex has option of developing the drug itself. Development costs are estimated at Rs. 7.5 million. After that the probability of success will be 50%.

If the product is successfully developed, Apex can sell the rights of developed product. Estimate is it can sell rights of developed product at Rs. 28 million with 40% probability and at Rs. 20 million with 60% probability.

Another option available after successful development for Apex is to market the drug itself. The possible revenues will be Rs. 10 million, Rs. 20 million and Rs. 48 million with probabilities of 0.3, 0.5 and 0.2 respectively.


Lastly, if the attempt to develop the product is unsuccessful, Apex can still sell the rights but only for 1.25 million.


Represent all information on a decision tree and identify optimal decision for M/s A.    10.

  • Explain what is meant by:
    • Expected monetary value (EMV)
    • Expected payoff with perfect information (EPPI)
    • Expected value of perfect information (EVPI)      




Explain regret matrix in assignment problem                                                                                                     3

Explain ‘Hungarian method’ of solving assignment problem                                                                      3

Explain Unbalanced Assignment Problem                                                                                                           3             

Expalin Optimality in an Assignment problem.                                                                                                  3

Explain Restricted assignment problem, which is an unbalanced problem.                                          3

Q.5. A company produces two products P and Q. 1 unit of Product P requires 4 units of machine 1 and 4 units of machine 2. 1 unit of Product Q requires 2 units of machine 1 and 6 units of machine 2. Capacities of M1 and M2 are 32 units and 48 units respectively. Maximum market demand for P is 4 units. Profit per unit of P and Q is Rs. 6 and Rs.12 respectively. Obtain optimal solution. Solve by simplex method.


  • What is the optimal product mix and optimal profit?
  • Is this a unique solution or is there an alternate optimal solution? Justify.
  • What are the shadow prices of resources?
(d) Identify scarce and abundant resources as per the optimal solution. 15


JINALL CLASSES                                                                                                 M: 9970034772


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