Question

The two objective functions (Maximize 5x + 7y, and Minimize -5x - 7y) will produce the same solution to a linear programming problem. True/ False?

Answer 1

Answer: FALSE

Explanation:

A maximization problem with the objective of, Maximize f(x) subject to x S is equivalent to the minimization problem with the objective function, Minimize -f(x) subject to x S.

Let f(x,y) = 5x + 7y

then

-f(x,y) = -(5x+7y) = -5x-7y

So, maximizing f(x,y) is same as minimizing -f(x,y).

But the solution to the maximization problem = -1 times the solution of the minimization problem.

Hence the solution is not exactly the same. The numbers might be the same but the signs change and hence the values.