The mathematical theory behind linear programming states that an optimal solution to any problem will lie at a(n) of the feasible region.
a) interior point or center
b) maximum point or minimum point
c) corner point or extreme point
d) interior point or extreme point
e) none of these

Option C) corner point or extreme point

Step-by-step explanation:

Linear Programming:

Linear programming is an optimization(maximization or minimization) technique for a system of linear equations and a linear objective function. The objective function defines the quantity to be minimized or maximized.The goal of linear programming is to find the values of the variables that maximize or minimize the objective function.

Corner Point Theorem:

The corner point theorem states that the optimum value of the feasible region occurs at the corner point of the feasible region, thus the minimum or maximum value will occur at the corner point or the extreme point.

Thus,

The mathematical theory behind linear programming states that an optimal solution to any problem will lie at corner point or extreme point of the feasible region