Page 50 - DCOM303_DMGT504_OPERATION_RESEARCH

Unit 2: Linear Programming Problems

2.10 Keywords Notes

Constraints: A condition that a solution to an optimization problem must satisfy.
Feasible Region: The region containing solution.

Feasible Solution: If a solution satisfies all the constraints, it is called feasible solution.
Shadow Price: The amount that the objective function value changes per unit change in the
constraint.

2.11 Review Questions

1. Explain the linear programming problem giving two examples.
2. What are the essential characteristics of a linear programming model?
3. What do you understand by ‘Graphical Method’? Give its limitations.
4. Explain the graphical method of solving a Linear programming Model involving two
variables.
5. Define and explain the following:
(i) Optimum Solution
(ii) Feasible Solution

(iii) Unrestricted Variables
6. A firm manufacturers headache pills in two sizes A and B. Size A contains I grains of
aspirin, 5 grains of bicarbonate and 1 grain of codeine. It is found by uses that it requires
at least 12 grains of aspirin, 74 grains of bicarbonate and 24 grains of codeine for providing
immediate effect. It is required to determine the least number of pills a patient should take
to get immediate relief.
Formulate the problem as a standard LPP.

7. Consider a small plant which makes 2 types of automobile parts say A and B. It buys
castings that are machined, bored and polished. The capacity of machining is 25 per hour
for A and 40 hours for B, capacity of boring is 28 per hours for A and 35 per hour for B, and
the capacity of polishing is 35 per hour A and 25 hour of B. Casting for port A costs ` 2 each
and for part B they cost ` 3 each. They sell for ` 5 and ` 6 respectively. The three machines
have running costs of ` 20, ` 14 and ` 17.50 per hour.
Assuming that any combination of parts A and B can be sold, what product mix maximizes
profit?
8. A ship is to carry 3 types of liquid cargo – X, Y and Z. There are 3,000 litres of X available,
2,000 litres of Y available and 1,500 litres of Z available. Each litre of X, Y and Z sold fetches
a profit of ` 30, ` 35 and ` 40 respectively. The ship has 3 cargo holds-A, B and C of
capacities 2,000, 2,500 and 3,000 litres respectively. From stability considerations, it is
required that each hold be filled in the some proportion. Formulate the problem of loading
the ship as a linear programming problem. State clearly what are the decision variables
and constraints.
9. A company produces two types of pens, say A & B. Pen A is superior in quality while pen
B is of lower quality. Net profits on pen A and B are ` 5 and ` 3 respectively. Raw material
required for pen A is twice as that of pen B. The supply of raw material is sufficient only for

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