1. A factory has two production lines available to make a...

1. A factory has two production lines available to make a product. The first can produce one lot of the product in t1 hours at cost c1, and the second requires t2 hours and cost c2. The plant manager wishes to find the least costly way to produce b lots in a total of at most T hours. An integer number x1 will be produced on line 1, and integer number x2 on line 2. Identify each of the following for this design problem. (a) The decision variables (b) The input parameters (c) The objective function (d) The constraints (e) Assume that t1 = 10, t2 = 20, c1 = 500, c2 = 100, b = 3, and T = 40. whether x1 = 0, x2 = 3 is a feasible and/or optimal solution.

Transcript

00:01 Alright, so we have a nice little optimization problem here.

00:03 So we have product a and product b and we're told the profit of each of them so the profit of a we're told is $40 and the profit of b we're told is $50 per unit and we're told that production time for a so we have production time is two hours for a and three hours for b hours and then the other piece we're told is storage and these the amount of storage it takes to hold a unit of a is four square meters and squared and then we're told it's two square meters for product b and now we're told that the for demand we have to have the demand is such that we need at least one per day we need we need a needs to be greater than or equal to one at least one.

01:18 We're told it at least one per day and let's see.

01:23 Let's think about the constraints here we have on this scenario.

01:27 We're told that the factory factor has a maximum production time of 15 hours per day so the max production time is 15 hours per day and we're told the storage space is 20 square meters.

01:43 All right, so and the factory aims to maximize the profit, of course so we're gonna set up the linear programming so i'm going to do this so let's think about we have our profit our profit so it's return to maximize and we're gonna consider the quantities here and the quantity of a quantity of b so profit well, that is equal to profit is equal to 40 a plus 50 b now we have our constraints production time.

02:22 So time we've got 15 is we need it to be below or equal to fifth 15 such that we have to a number of a plus three times number b.

02:35 We add take that some that has to be less than equal to 15 that's our time.

02:40 Then we have our storage space we have a maximum of 20 so that's greater than or equal to 4 a plus 2 b and of course demand has to be bigger than so now let's go ahead and and do this.

02:56 We i did this in excel a little optimization problem here and here we go.

03:06 So it's the chart very i mean it i set up the chart just like we talked about second ago here's the profit production time storage demand.

03:12 These are fixed quantities these are gonna change but here's those production times and what i'd have here.

03:17 This is the the the quantity multiplied by its production time storage quantity times the storage and then the profit the 90 in this case is i just this is the starting values that's 40 times the quantities 50 times the quantity for b and so on so forth.

03:33 That's what those are and excel has a great little solver program in here.

03:38 It's gonna do that...

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