Attempt all the problems.

Section-A

problem1) Describe using two applications for Goal Programming.

problem2) Describe using two applications for Sensitivity analysis in Linear Programming.

problem3) Solve the following Linear Programming Problem using Simplex method.

Minimize Z = 36A + 60B + 45C

Subject to constraints:

A + 2B + 2C ≥ 40
2A + B + 5C ≥ 25
A + 4B +  C ≥ 50
A , B, C   ≥ 0

problem4) Company produces two types of hats. Each hat of first type requires twice as much labour time as the second type. If all hats of second type only, the company could produce the total of 500 hats a day. The market limits daily sales of first and second type of hat to 150 and 250 hats respectively. Suppose the price per hat are Rs. 8 each for Type A and Rs. 5 each for type B, formulate problem as a linear programming problem in order to determine the number of hats so as to maximize the profit. 

a) Formulate the above as Linear programming problem

b) Solve the above problem using Graphical Technique.

Section-B

Local travel agent is planning charter trip to a major sea port. Eight day/seven night package includes fare for round trip, surface transportation, board and lodging and selected tour options. Charter trip is restricted to 200 persons and past experience indicates that there would not be any problem for getting 200 clients. Problem for travel agent is to find out the number of Deluxe , Standard and Economy tour packages to offer for this charter. These three plans differ according to seating and service for the flight, quality of accommodations, meals plans and tour options. The following table summarizes the estimated prices for the three packages and the corresponding expenses for the travel agent. The travel agent has hired an aircraft for a flat fee of Rs. 2,00,000 for the entire trip.

In planning trip the following considerations should be taken into account.

(I) At least 10% of the packages should be of the Deluxe type

(II) At least 35% but not more than 70% should be of the standard type

(III) At least 30% should be of the Economy tupe.

(IV) The maximum number of Deluxe packages available in aircraft is restricted to 60

(V) The Hotel desires that at least 120 of the tourists must be on Deluxe and Standard packages taken together.

Price and Cost for tour packages per person.

Tour Plan     Price        Hotel Costs      Meal and Other Expenses
Deluxe       10000           3000                 4750
Standard     7000            2200                 2500
Economy     6500           1900                  2200

Travel agent needs to determine number of packages to offer in each type so as to maximize the total profit. Formulate this as a Linear Programming problem.