Consider the following statements about linear programming problems (LPP):
(A) The decision variables of an LPP are taken to be continuous, controllable and non-negative.
(B) The conditions \(x \ge 0\), \(y \ge 0\) on the decision variables are sometimes called trivial constraints.
(C) In a diet problem, the cost of the diet is the objective function, and it is to be maximised.
(D) In a transportation problem, the constraints come from the supply at the sources and the demand at the destinations.
Choose the correct answer from the options given below:
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → (A), (B) and (D) only
An LPP has three parts: the decision variables, the objective function and the linear constraints. The decision variables stand for quantities the decision-maker controls, so they are continuous and cannot be negative.
So the deciding facts are: the variables are continuous, controllable and non-negative; \(x \ge 0, y \ge 0\) are the trivial constraints; a diet problem minimises cost; a transportation problem is limited by supply and demand.
Checking the statements
(A) The decision variables of an LPP are taken to be continuous, controllable and non-negative. — Correct. These are the three properties assumed for decision variables.
(B) The conditions \(x \ge 0\), \(y \ge 0\) on the decision variables are sometimes called trivial constraints. — Correct. The non-negative restrictions are also known by this name.
(C) In a diet problem, the cost of the diet is the objective function, and it is to be maximised. — Incorrect. The diet must give the needed nutrients at the least cost, so the cost is minimised.
(D) In a transportation problem, the constraints come from the supply at the sources and the demand at the destinations. — Correct. The supply and demand patterns give the constraints, and the transport cost is minimised.