Question

What is the difference between the optimal solution to a linear programming problem and the objective function value at the optimal solution? Use an example in your explanation

Answer 1

An optimal solution is a feasible solution where the objective function reaches its maximum (or minimum) value – for example, the most profit or the least cost. A globally optimal solution is one where there are no other feasible solutions with better objective function values. A locally optimal solution is one where there are no other feasible solutions “in the vicinity” with better objective function values – you can picture this as a point at the top of a “peak” or at the bottom of a “valley” which may be formed by the objective function and/or the constraints. Whereas, Linear programming (LP) is one of the simplest ways to perform optimization. It helps you solve some very complex optimization problems by making a few simplifying assumptions. As an analyst, you are bound to come across applications and problems to be solved by Linear Programming.For some reason, LP doesn’t get as much attention as it deserves while learning data science. So, I thought let me do justice to this awesome technique. I decided to write an article that explains Linear programming in simple English. I have kept the content as simple as possible. The idea is to get you started and excited about Linear Programming.

Example:

In maximization problem, optimal solution occurring at corner point yields the

A . mean values of z

B . highest value of z

C . lowest value of z

D . mid values of z

Let Q be the feasible solution for a linear programming problem and let Z = ax + by be the objective function. When Z has an optimal value (maximum or minimum), where the variables x and y are subject to constraints described by linear inequalities, this optimal value must occur at a corner point (vertex) of the feasible region.

for a maximization problem, the optimal value occurring at the corner point yields the highest value of Z.

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