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In this problem we have to find the linear programming problem by graphical method.
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The objective function is given as objective function is z is equal to 2x plus 3y subject to the constraints.
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2x plus y greater than or equal to 30 x plus 2y greater than or equal to 24 and x comma y greater than or equal to 0.
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So first we have to solve this by graphical method.
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So first we will consider the first constraint that is 2x plus y greater than or equal to 30.
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We will make it as an equality constraint.
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So if we take x equal to 0, then y will be 30.
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And when we take y equal to 0, x will be 15, right? then consider the second constraint, x plus 2y equal to 24 x, y.
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So we will take x as 0.
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So y is equal to 12.
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When we are taking y equal to 0, then x we may get it as 24.
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Okay, so now we have to plot these values.
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Draw x -axis and y -axis, x -axis, x -axis, and the units we can take it as 5, 10, 15, etc.
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And in y -axis also, we will consider the same.
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5, 10, 15, 20, 25, 30, 20, 25, 30, etc.
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So now we will plot the points first one 030.
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So here we may get it.
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Next one 15 .0.
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Now we have to join these two points and it is given.
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This line is 2x plus y greater than equal to 30 and the constraint is greater than or equal to constraint.
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So we are considering this portion right.
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So above the line we are considering.
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Next one x plus 2y greater than or equal to 24...