This question has infinitely many solutions, how do we get to that conclusion? I used graph to solve it but it gave me single answer. Any help will be highly appreciated!
Linear programming: infinite solutions
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linear-programming
1 Answers
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The easiest way to see this is that your objective $$z = (1/2)x +(3/2)y $$ is proportional to one of your constraints: $$2z = x+3y \le 15.$$ Thus along the piece of your boundary on which this constraint is in effect, your target function is constant and has the value $z = 15/2$.
When you compute the objective at each extreme point, you find that $z=15/2$ is the largest value and it is obtained at both $(0,5)$ and $(3/2,9/2)$. The line segment between them is where the above constraint is in effect so $z$ has its maximum value on this entire line segment, i.e. for an infinite number of values.