Match List-I with List-II
| List-I | List-II | ||
|---|---|---|---|
| Description | Assumption of a linear programming problem | ||
| (A) | The available resources, the profit per unit and the resource used per unit are all known and fixed. | (I) | Additivity |
| (B) | The decision variables may take fractional values as well as whole-number values. | (II) | Certainty |
| (C) | The contribution of each variable to the objective function and to each constraint is directly proportional to its value. | (III) | Proportionality |
| (D) | The total profit is the sum of the separate profits contributed by the decision variables. | (IV) | Divisibility |
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → (A)-(II), (B)-(IV), (C)-(III), (D)-(I)
A linear programming problem rests on four basic assumptions.
(A) The available resources, the profit per unit and the resource used per unit are all known and fixed.
This matches (II) Certainty: every number in the problem is known exactly.
(B) The decision variables may take fractional values as well as whole-number values.
This matches (IV) Divisibility (also called continuity).
(C) The contribution of each variable to the objective function and to each constraint is directly proportional to its value.
This matches (III) Proportionality: doubling x doubles its profit and the resources it uses.
(D) The total profit is the sum of the separate profits contributed by the decision variables.
This matches (I) Additivity.