The constraints of a problem are listed below. what are the vertices of the feasible region? x+3y≤6 4x+6y≥9 x≥0 y≥0 a) (-3/2,5/2), (9/4,0), (6,0) b) (0,0), (0,3/2), (9/4,0) c) (0,0), (0,2), (6,0) d) (0,3/2), (0,2), (6,0), (9/4,0)

ANSWER

The correct answer is D

EXPLANATION

To graph the inequality

we first graph the corresponding equation,

We then test the origin to determine which half-plane to shade the inequality,

The above statement is true so we shade the lower half plane.

Next, we graph

By first graphing the corresponding equation,

Then we test the origin again,

This statement is false, so we shade the upper half plane

Next, we graph,

Draw the vertical line and shade to the right.

Finally, we graph,

Draw the horizontal line and shade the upper region.

the intersection of all the shaded regions is called the feasible region.

The four vertices of the feasible region are

Hence the correct answer is D

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