Question

Feasible region’s optimal solution for a linear objective function always includes
(a)downward point
(b)upward point
(c)corner point
(d)front point

Answer 1

Hint: As we know that feasible regions are an important part of linear programming. WE know that there are different feasibility conditions in linear programming problems. Linear programming is an optimization problem for which we try to maximize or minimize the linear function of a decision variable. A feasible solution to linear programming problems must satisfy all of the problems constraints simultaneously .

Complete step by step solution:
We know that a feasible region’s optimal solution must be a corner point of the feasible region and must optimize the value of the objective function.
To solve the linear programming problem and finding the feasible region, we use the linear inequalities to find them, denoted by the sign $( \leqslant , \geqslant )$. There will be constraints given like: $x \geqslant 0,x + y \leqslant 6,y \leqslant x + 3$ and then we check for the feasible region and find the optimal value.
Therefore a feasible region’s optimal solution for linear objective function always includes corner points.
Hence the correct option is (c)corner point.
So, the correct answer is “Option C”.

Note: We should note that some linear programming problems do not have any feasible region. Sometimes different constraints form different areas, which are common and thus we cannot consider them as feasible regions. We have to consider every constraint to find the required feasible region in linear programming problems.