Question

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Answer 1

erp, sorry. Should be y = 5 - x

5 = y + x
5 - x = y
y = 5 - x

Answer 2

ignore that for a sec, sorry. I'll repost it in a sec.

To solve that, you plug the value for y into that other equation

y = 5 - x
y = 1/3 x + 3

therefore

5 - x = 1/3 x + 3

Answer 3

you solve for x.

1/3 x + x = 5 - 3

Answer 4

So there you factor out the x, then divide to get x by itself

x ( 1/3 + 1 ) = 5 - 3

x = (5-3) / (1/3 + 1)

Answer 5

so there, you can make it easier by putting the 1 in fraction form with a 3 on the bottom to add to the 1/3

1 = 1/1 = 3/3

\[\frac{ 3 }{ 3 } + \frac{ 1 }{ 3 } = \frac{ 3 + 1 }{ 3 }\]

Answer 6

Then \[\frac{ 5 - 3 }{ \frac{ 1 + 3 }{ 3} } = \frac{ (5 - 3) 3 }{ 1+3 }\]

Answer 7

I gotta run, plus I think I'm complicating things. Sorry.

To get the solution, you have to solve the two inequalities (I found it easier to do the opposite of what I just showed, and

solve for x ----> x ≤ 5 - y

Then put in into the other inequality (So where it says x, just put that 5 - y in)

Then that should give you the other two vertices you don't know (The first two are x ≥ 0 and y ≥ 0).

Then, find the biggest value of x and y allowed within the region (remember that x + y has to be smaller than or equal to 5 given the last constraint), and then put those numbers into C = 6x - 4y to solve for C.

You want C as big as it can be.

Anyway, good luck, and I can delete all of this convoluted mess if you want :)