Question

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 1

D)

Explanation:

Source: Trust me bro

Answer 2

The correct answer is D

EXPLANATION

To graph the inequality

`x+3y\le 6`

we first graph the corresponding equation,

`x+3y= 6`

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

`0+3(0)\le 6`

`0\le 6`

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

Next, we graph

`4x+6y\ge 9`

By first graphing the corresponding equation,

`4x+6y=9`

Then we test the origin again,

`4(0)+6(0)\ge 9`

`0\ge 9`

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

Next, we graph,

`x\ge 0`

Draw the vertical line
`x=0` and shade to the right.

Finally, we graph,

`y\ge 0`

Draw the horizontal line
`y=0` 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

`(0,(3)/(2)),(0,2),(6,0),( (9)/(4),0)`

Hence the correct answer is D