Question

A feasible solution to an LP problem:
(a) must satisfy all of the problem’s constraints simultaneously.
(b) need not satisfy all of the constraints, only some of them.
(c) must be a corner point of the feasible region.
(d) must optimize the value of the objective function.

Answer 1

In the above problem, we are asked to write about the feasibility of linear programming (LP) problems. There are different feasibility conditions given in the options in the above problem and we have to mark the correct option(s).

Complete step-by-step solution:
A linear programming (LP) problem is an optimization problem for which we are trying to maximize (or minimize) a linear function of the decision variables. This function of the decision variables is known as the objective function. So, we can say that LPs optimize the value of the objective function. This means the option (d) in the above problem is correct.
Now, a feasible solution to the LP problem must be satisfying all the constraints simultaneously. This means the option (a) in the above problem is correct.
The feasible region in the LP is a set of feasible solutions that could be possible for an L.P. And the optimal solution of an LP is the extreme (corner) point in the feasible region. Hence, the option (c) is correct.
From the above discussion, we have found that options (a), (c), and (d) are the correct options.

Note: Generally, we got confused about whether a feasible solution of a linear program will satisfy all the constraints simultaneously or a few of them. The answer is a feasible solution of a linear program that always satisfies all the constraints because a linear program is an algorithm, which will satisfy the objective function so a feasible solution must satisfy all the constraints of a linear program.