Carco manufactures cars and trucks. Each car contributes 300...

Carco manufactures cars and trucks. Each car contributes $300 to profit and each truck, $400. The resources required to manufacture a car and a truck are shown in the table below. Each day, Carco can rent up to 98 Type 1 machines at a cost of $50 per machine. The company now has 73 Type 2 machines and 260 tons of steel available. Marketing considerations dictate that at least 88 cars and at least 26 trucks be produced. Vehicle Days on Type 1 Machine Days on Type 2 Machine Tons of Steel Car 0.8 0.6 2 Truck 1 0.7 3 Find the optimal solution and the sensitivity analysis using Excel. Show the steps.

Transcript

00:01 Okay, so basically here in the question they gave that, one second, i'm opening it, yeah, they gave that the factory manufacturers, electric cars and delivery trucks.

00:17 I'm assuming it to be, you know, i'm assuming cars to be as c and trucks to be as t.

00:22 Also, they gave that they require two shops, you know, assembly shop and a part shop.

00:32 So, paint.

00:33 Shop, okay, paint shop.

00:36 So basically, this particular work will be done.

00:41 You know, the car and the assembly shop will have a time of, will take a time of one by 50th of the day.

00:50 So this is the this is the chat they already mentioned.

00:55 So basically, so basically they also mentioned about the profits which becomes our objective function.

01:06 We have to maximize the profits.

01:08 And i'm assuming this particular profits to be as z.

01:13 So the profit per truck is 300.

01:16 So 300 times t plus 225 times t.

01:22 Okay.

01:23 What do we have to find? we have to find the number of trucks at the optimum solution, number of cars at optimum solution and the optimal solution value.

01:31 So for that we have to first drive this particular data in the equal equation form.

01:39 So how can i write that? p divided by 50 plus t divided by 50.

01:48 Okay, has to be less than one.

01:50 Because we are dealing with per day profits.

01:55 So the other equation would be this.

02:00 Correct? let me choose another another color to plot.

02:10 I would use orange that is better.

02:13 So if this this is p and if this is p you know x -axis let x -axis be cars and y -axis be truck so what do we get we get a straight line equation 50 50 5 this is okay this is the area for this particular equation correct but then i'm not interested in this area because this has to satisfy both the equations you know both the workshops as to the other equation also so let's say somewhere around 25 i'm going to draw so let's just say that this is so this is the area this particular this particular area is for the second part by the way i forgot to tell you cars number of cars cannot be negative so she is greater than to 0 and please reddena level to 0 correct so we have to plot only in the first quadrant that is also there.

03:29 So the common area is this one.

03:34 Okay? so let me go back to the black ink.

03:40 So this is the point we have to find out.

03:42 This is the point we have to find out.

03:44 And yeah, using the graphical method, these are the points where optimum maltuckert.

03:50 So basically we know this particular point that's 20, 0 comma 25...

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