Linear Programming - Help needed desperately!

[Denied]

Here's the problem:

It takes two hours of cutting and four hours of sewing to make a casual suit and four hours of cutting and two hours of sewing to make a formal suit. You can only have 20 hours of cutting and 16 hours of sewing. The profit is $47 for a casual suit and $61 for a formal suit.

I can't seem to figure out how to make the equation. I've been working on this problem for a long time, and all I have so far is this, but I'm not even sure it's right. On top of that, I have to graph it... and I don't understand how. Someone please help me.

x = cutting
y = sewing
a = casual suit
b = formal suit

2x+4y=a
4x+2y=b
x<20
y<16

 

[mmm4444bot]

Forget a and b. You're graphing on an xy-coordinate system.

Let x = the number of casual suits produced

Let y = the number of formal suits produced

These are the numbers that you're asked to find, correct? In other words, how many casual and formal suits will maximize profit?

2x + 4y represents the total number of cutting hours required to produce x casual suits plus y formal suits.

Therefore, we have:

2x + 4y ? 20

Likewise, from the sewing-hours constraint, we have:

4x + 2y ? 16

You are correct that we also have:

x ? 0

y ? 0

So, solve each of the following equations for y, and graph each line.

2x + 4y = 20

4x + 2y = 16

[attachment=0:3lpjrms9]linears.JPG[/attachment:3lpjrms9]

Ignoring (0, 0), we see that there are three points of interest (the vertex points of the closed four-sided region formed):

[point 1] The y-intercept of the red line.

[point 2] The lines' intersection point.

[point 3] The x-intercept of the green line.

Now, profit is given by:

P = 47x + 61y

To find the maximum profit, substitute each of the (x, y) values from the three points of interest into the formula for P; that is, evaluate P, and compare the results.

(0, 5) leads to P = 305

(2, 4) leads to P = 338

(4, 0) leads to P = 188

We find that the suitmaker reaps the greatest profit by making two casual suits and four formal suits.

 

[mmm4444bot]

(heh, heh, heh, heh, heh)