Question

Given the system of constraints, name all vertices of the feasible region. Then find the maximum value of the given objective function. constraints{ x>0 y>0 y<1/3x +3 5>y+x} Objective function C=6x-4y

Answer 1

Did you graph all those constraints yet?

Answer 2

no i havnt. So far i have (0,0)

Answer 3

The region is a quadrilateral with 4 vertices.
Question: are all those inequalities '<' or '>,' or are they actually '≤' and '≥?'

Answer 4

they are the last 2, i dont now how to put those in on computer tho

Answer 5

There are ASCII codes for them, but you can type <= for ≤ and >= for ≥.
Ok, that's good because otherwise the vertices themselves wouldn't be in the region, but since they are, you can use them.
You know the theorem that maximum objective values occur at vertices, and that's why you have to find them first, right?

Answer 6

Yes, i know that. Im confused though how to find the vertices tho

Answer 7

So, yeah, you have four lines to plot. Draw a coordinate grid, or use graph paper, or just throw down some X- and Y-axes, and graph the four given lines.

Answer 8

The four lines are
x=0
y=0
y=x/3+3
y=-x+5

The direction of the < or > shows where to shade in.

Answer 9

so at (0,0) i shade down to all negatives?

Answer 10

No, this is restricted to fourth quadrant; the first two constraints are x≥0 and y≥0.
All the numbers will be positive here.