problem 1)a) describe briefly various O.R. models, their applications and limitations.

b) A soft drink plant has two bottling machines A and B. A is designed for 8 oz bottle and B for 16 oz bottle. However each can be used on both types as per the table given below:.

                 8 oz bottle                                                    16 oz bottle
Machine A    100/ min                                                           40/min
Machine B     75/min                                                             60/min

The machines can be run8 hrs/day, 5 day/week. Weekly production cannot exceed 300,000 oz Market can absorb 25,000 of 8 oz bottle and 7000 of 16 oz. bottle. Formulate LPP and draw the first simplex tableau. Do not solve.

problem2)a) describe the following special cases of LPP with exs: i) Multiple optimal solutions (ii) Unbounded problem.

b) A hotel has 110 similar bed rooms , each of which can occupied by either one or two persons. Rent for one person is $ 80 per day and for two persons, the rent is $ 100 per day. The dining room ( which is exclusively used for hotel guests) has a maximum capacity of 160. Each room is serviced daily. If it has a single occupant, the time taken is 15 minutes , but a room with two occupants takes 20 minutes to service.

(i) What mix of single and double room bookings should the hotel aim for?. Use simplex algorithm. (ii) Conduct sensitivity analysis w.r.t. R.H.S.values and objective function coefficients. (iii) What would be your reactions to the alternative proposals: a) build an annex with another 5 bed rooms or b) extend the dining room capacity to 180 or c) employ an extra maid for one hour per day? What is the limit on extra time that could be profitably used under ( c )?

3A)

Solve the following transportation problem:

      Destination
                     1    2    3    supply
Origin       A   10  16  12     25
               B    7   11  11     20
               C    7    9    8      15
Demand:       20  27   13

Does the above problem have multiple solution? If so, identify the alternate optimum.

3B)

A local authority has five contracts to be allocated to five firms that have submitted tenders. Each firm will be awarded exactly one contract.. The tender amount submitted (in units of million Rupees) are:

Contract       1    2     3         4      5
Firm        A   7    7     3         6     10
              B   8    9   No bid    5     8
              C   9    11  13        10    13
              D   6    6     8     No bid  12
              E    5    5     9        10    11

Which contract should go to each firm in order to minimize the overall cost? Use assignment algorithm.