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BEC-2153 – Management Science - Management Science Assignment Help

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Added on: 2021-07-12 13:56:28
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Question Task Id: 306515
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1. A diet conscious housewife wishes to ensure certain minimum intake of vitamins A, B and C for the family. The minimum daily (quantity) needs of the vitamins A, B , C for the family are respectively 80, 100 and 70 units. For the supply of these minimum vitamin requirements, the housewife relies on two fresh foods. The first one provides 4, 2, 2 units of the three vitamins per gram of the foodstuff respectively and the second one provides 2, 4, 2 units of the same three vitamins per gram of the foodstuff respectively. The first foodstuff costs Rs. 8 per gram and the second Rs. 6 per gram. Using the graphical method find the grams of each foodstuff that should be bought by the housewife everyday to keep her food bill as low as possible.

2. Write down the Standard format for the following linear programming problem.
Maximize Z = 4x1 + 3x2 + 5x3
Subject to x1 + 3x2 + 2x3 ? 10
 2x1 + 2x2 + x3 ? 6
 x1 + 2x2 + 3x3 =14
 x1 , x2, x3 ? 0

3. A manufacturer produces four products A, B, C and D each of which is processed on three machines P, Q and R. Availability of machine hours and profit contributions per unit are given as follows.
Time required in hours per unit Availability in hours
Machine P 1.5 2 4 3 550
Machine Q 4 1 2 1 700
Machine R 2 3 1 2 200
Profit per unit
4 6 3 1

4. A product is produced by four factories A, B, C and D. Their production capacities are 50, 70, 30 and 50 units respectively. These factories supply the product to four stores, demands of which are 40, 35, 105, and 20 units respectively. Unit transport cost in rupees from each factory to each store is given in the table below.
1 2 3 4
A 4 6 8 13
B 13 11 10 8
C 14 4 10 13
D 9 11 13 8
(a) Find an initial solution using Vogel’s approximation method.
(b) Find the optimum solution for the above problem using MODI method.


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