00:01
Okay, in this problem we have a furniture company that produces regular kitchen cabinets, which we're going to use y for and varnished cabinets, which we're going to use y for.
00:20
So x regular y varnished.
00:25
And we want to find a linear program to describe this situation that's written.
00:37
And then we want to find the optimal solution to our linear problem.
00:43
So i'm going to start by drawing a little bit.
00:48
We're going to start by the end.
00:50
So we know we want to maximize profits.
00:55
And we know that it costs, the profit for a regular cabinet is 100.
01:04
And the profit for a varnish cabinet is 150.
01:08
So that's our cost function.
01:10
I'm going to write it as c of x and y.
01:21
We know, so that's what we want to do, but there are constraints to our problem that will be easier to visualize if we use a graph.
01:33
We have x and y axes.
01:38
Now we know that the maximum capacity for regular cabinets is 200.
01:45
So we know that our line x cannot be greater than 200 so we will be on this side y is 250 we know it cannot be greater than this so we're going to be under so right now we have a box so we know that x smaller or equal to 200 and we know that y is smaller or equal to 150.
02:40
Finally, another constraint is that varnishing a unit take twice as much time as painting a regular unit.
02:58
So it's to produce one which we can rewrite this constraint like this so it takes twice as much time or by the time we paint sorry about that so when we produce two regular one it gives us we have time to produce one varnished once so that will limit where we can find solution.
03:42
So i'm going to draw another line which we're going to be around here.
03:49
So i'm going to make it a bit longer...