Question 76536
I was actually teaching this to a bunch of first year degree students, only a couple of weeks ago. If you're interested, this is how you begin a linear programming problem. Anyway. The first thing to do is identify our variables - this really only comes with practice, but normally you will find (at least in simple problems) the variables rae normally the things you can make.<br />

In this case we have the number of bouquets (x) and the number of wreaths (y)<br />

OK, the bouquests take 1 hour each to produce, and the wreaths take 2, so the amount of time to produce x bouquets and y wreats is *[tex x+2y] right? Now, labour is at a maximum of 80 hours so our first inequality is simply<br />

*[tex x+2y\leq 80]

The total production capacity is the amount of things we can make, yeah? so if we make x bouquets and y wreaths, then we make x+y things, agreed? We can make a maximum of 60 things so our next inequality is<br />

*[tex x+y\leq 60]

WE must also never forget the non-negativity inequalities. Clearly we can't make -5 wreaths or -3 bouquets, so we also have<br />

*[tex x\geq 0]
*[tex y\geq 0]

Now you have the inequalities, see if you can graph them. I think someone has written a lesson on here about graphing inequalities, so if you get stuck have a read of that. Or if that fails come back.

Hope that helps,
Kev