Page 30 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 2: Linear Programming Problems

Solution: Notes
Let x be the no. of nurses working during period 1
1
x be the no. of nurses working during period 2, and
2
x , x , x and x be the no. of nurses working during period 3,4,5, and 6 respectively.
3 4 5 6
Hence, the objective function is given by,
Minimise ‘C’ = x + x + x + x + x + x (Subject to constraints)
1 2 3 4 5 6
x + x  2
1 2
x + x  7
2 3
x + x  15
3 4
x + x  8
4 5
x + x  20
5 6
x + x  6
6 1
x , x , x , x , x , x  0 (Non-negativity constraints)
1 2 3 4 5 6

Notes Steps of linear programming model formulation are summarized as follows:
Step 1: Identify the decision variables
Step 2: Identify the problem data

Step 3: Formulate the constraints
Step 4: Formulate the Objective Function

Task Formulate the following as LPP
One of the interesting problems in Linear Programming is that of balanced diet. Dieticians
tell us that a balanced diet must contain certain quantities of nutrients such as proteins,
minerals, vitamins, etc. Suppose that you are asked to find out the food that should be
recommended from a large number of alternative sources of these nutrients, so, that the
total cost of food satisfying minimum requirements of balanced diet is the lowest. The
medical experts and the dieticians tell us that it is necessary for an adult to consume at least
75 gms. of proteins, 85 gms. of fats and 300 gms. of carbohydrates daily. The following
table gives the different items (which are readily available in the market); Item analysis
and their respective costs.
Formulate this problem as LPP
Food volume (per 100 gms.) Cost/Kg.
Food
Proteins Fats Carbohydrates (`)
1 8 1.5 35 1
2 18 15 __ 3
3 16 4 7 4
4 4 20 2.5 2
5 5 8 40 1.5
6 2.5 __ 25 3
Minimum daily requirements 75 85 300

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