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  4. Consider the graph of constraints stated as linear inequalities as below 5 x+y ≤ 100 ...(i) x+y ≤ 60 ...(ii) x ≥ 0 ....(iii) y ≥ 0...(iv) <img class=img-fluid question-image alt=image src=https://cdn.tardigrade.in/img/question/mathematics/b714546797c6149a8a2ea38e0972f1d9-.png /> where, x and y are number of tables and chairs on which a furniture dealer wants to make his profit. The shaded region in the graph is called

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Q. Consider the graph of constraints stated as linear inequalities as below
$5 x+y \leq 100 $...(i)
$ x+y \leq 60 $...(ii)
$x \geq 0 $....(iii)
$y \geq 0$...(iv)
image
where, $x$ and $y$ are number of tables and chairs on which a furniture dealer wants to make his profit.
The shaded region in the graph is called

Linear Programming

Solution:

Constraints are
$5 x+y \leq 100 $...(i)
$ x+y \leq 60 $...(ii)
$x \geq 0 $....(iii)
$y \geq 0$...(iv)
image
The graph of this system (shaded region) consists of the points common to all half planes determined by the inequalities (i) to (iv). Each point in this region represents a feasible choice open to the dealer for investing in tables and chairs. The region, therefore, is called the feasible region for the problem.