Woodco produces desks and chairs. The unit profit, the wood...

Woodco produces desks and chairs. The unit profit, the wood used (in square feet), and the number of skilled carpentry hours used to produce a desk or a chair are given in the table below. Assume there are 1200 square feet of wood and 600 hours of carpentry available, and the demand is unlimited. Unit profit Wood used Carpentry hours used Desk Chair $250 $150 22 18 14 8 Find the number of desks and chairs that maximize the profit.

Transcript

00:02 All right, so here in this problem, we have this furniture company, and it's telling us that, trying about my new whiteboard here, x1 equals the quantity of tables, x2 is the chairs, and x sub 3 is the bookcases, number of bookcases that it's going to make.

00:36 All right.

00:38 So, knowing that, those are the first question says, or second question is, what are the decision variables? these are called the decision variables.

00:54 Okay.

00:55 So when you go to answer question b down at the bottom, it says, you know, these are what we call the decision variables.

01:02 We want to figure out the quantity of the tables, the quantity of the chairs, and the quantity of cases we need to make in order to maximize our profit.

01:12 So question a saying what's the purpose is to maximize profit.

01:20 All right.

01:25 The decision variables, as i was just mentioning, are the number of tables, chairs, and bookcases we need to make.

01:32 So the answer to question b, it's number of tables, number of chairs.

01:46 It's the x1.

01:47 X2, all that.

01:50 And the number of bookcases.

01:56 All right.

01:58 So that's part b.

01:59 Now, part c is what are the system constraints? all right, that's all the things that limit us.

02:06 Like, obviously, we can't just use an infinite number of hours of work.

02:11 We're limited by the number of employees we have, the time they can work, things like that.

02:16 So our limits are the amount of labor, hours of labor.

02:27 And that's limited to 60 hours.

02:29 Now, that could be five guys each work in 12 hours.

02:32 It could be, you know, 10 guys each work in six hours.

02:38 You know, it's just a number of total hours that we can use.

02:43 So that's the first one.

02:44 The next one is the time on the machine.

02:47 Machine time, right? labor has to be less than or equal to 60.

02:57 The machine time, the machine can only run for so many hours.

03:03 Oh, there you go.

03:05 So the machine time has to be less than or equal to 16.

03:11 The wood, the materials, our wood, has to be less than or equal to 400 feet.

03:19 Okay? so, you know, and now we don't know these numbers, but in order to, you know, make a bookcase, we're going to have to use the machine for so many hours.

03:29 In order to make a chair, we have to use the machine for so many hours.

03:33 In order to make a table, we've got to use the machine for so many hours.

03:37 Also, when we build a chair, that's going to take a certain amount of time...

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