A linear programming problem is shown below:

$Maximum: Z = 2 x + 3 y$

$Subjected to;$
$4 x + 6 y \leq 24$
$5 x + 4 y \leq 20$
$x, y \geq 0$
It has

no solution

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exactly one optimal solution

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an unbounded objective function

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infinitely many optimal solution

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Solution

The correct option is D infinitely many optimal solution
Objective function is parallel to one of the binding constraints.

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Similar questions

Maximize 3x + 7y

Subject to

3 x + 7 y \leq 10

4 x + 6 y \leq 8

x, y \geq 0

It has

Z = 5 x + 3 y

3 x + 5 y \leq 15, 5 x + 2 y \leq 10, x \geq 0, y \geq 0

Z = 60 x + 30 y

2 x + 3 y \geq 120

2 x + y \geq 80

x \geq 0, y \geq 0

Z = 7 x + 10 y

4 x + 6 y \leq 240

6 x + 3 y \leq 240

x \geq 10

x \geq 0, y \geq 0

Z = 7 x + 10 y

4 x + 6 y \leq 240 6 x + 3 y \leq 240 x \geq 10 x \geq 0, y \geq 0

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