ITM341
Advanced
Operations Research
(For CNM
Cases)
Assignment - I
Assignment Code: 2016ITM341A1 Last Date
of Submission: 30th April 2016
Maximum
Marks: 100
Attempt all the questions.
All the questions are compulsory and carry equal marks.
Section-A
1 Explain using two applications
for Goal Programming
2 Explain using two applications
for Sensitivity analysis in Linear Programming
3 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
4 A company produces two types of
hats. Each hat of the first type requires twice as much labor time as the second type. If all hats of the
second type only, the company can produce a total of 500 hats a day. The market limits daily sales of the first
and second type of hat to 150 and 250 hats
respectively. Assuming the price per hat are Rs. 8 each for Type A and Rs. 5
each for type B, formulate the
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 a Linear programming problem
b) Solve
the above problem using Graphical Technique.
Section-B
A
local travel agent is planning a charter trip to a major sea port. The eight
day/seven night package includes the fare for round trip, surface
transportation, board and lodging and selected tour options. The charter trip
is restricted to 200 persons and the past experience indicates that there will
not be any problem for getting 200 clients. The problem for the travel agent is
to determine 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 the trip the following considerations must be taken into account.
(I)
At least 10% of the packages must be of the
Deluxe type
(II)
At least 35% but not more than 70% must be of
the standard type
(III)
At least 30% must be of the Economy tupe.
(IV)
The maximum number of Deluxe packages
available in any aircraft is restricted to 60
(V)
The Hotel desires that at least 120 of the
tourists should be on the 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
|
The travel agent wishes to determine the number of packages
to offer in each type so as to maximize the total profit. Formulate
this as a Linear Programming problem.
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