An industrial system involves manufacturing transportation...

An industrial system involves manufacturing, transportation, and agriculture. The interdependence of the three industries is given by the input-output matrix shown on the right. M T A 0.2 0 0.08 M 0 0.5 0.05 T 0 0.5 0.85 A At what levels must the industries produce to satisfy a demand for manufactured goods, transportation, and agricultural products, respectively, given in the demand matrix to the right? Upper D equals left bracket Start 3 By 1 Matrix 1st Row 1st Column 80 2nd Row 1st Column 100 3rd Row 1st Column 180 EndMatrix right bracket Question content area bottom Part 1 Production levels of enter your response here units of manufacturing, enter your response here units of transportation, and enter your response here units of agriculture are needed.

Transcript

00:01 In this question it is given that our matrix of the form, here we have 0 .8, here we have 0, here we have 0 .05, here we have 0 .5, here we have 0 .5, here we have 0 .15, here we have 0 .15, here we have 0 .5, here we have 0 .625.

00:32 Well, this represents m, this represents t, this represents a, whereas this represents m, this represents t and this represents a, where it is manufacturing and t is transportation, a is agricultural.

01:15 There is one more matrix given to us as the demand matrix which we are going to represent by d, that is 160.

01:37 Here we have 180, here we have 160.

01:43 So here we need to find production, level of manufacturing, transportation and agriculture.

02:12 So here for evaluating it, we consider.

02:18 Construct the augmented matrix as here we have a x is equals to d that is here we have a as 0 .8 0 0 .05 here we have 0 .5 here we have 0 .5 here we have 0 .5 here we have 0 .25 here we have 0 .15 here we have 0 .1 25 here we have 0.

02:52 Here x represents m t a which is equals to 160 180 160 so now this can be further written as this so now by applying the row operation as r2 tends to r2 by 0 .5 and r3 tends to r3 by 0 .5 we get the matrix as this.

03:41 Now further on reduction, this can be written as.

03:47 This now by applying the row operation as r3 tends to r3 negative r2 we get the required matrix as this matrix can be written as 0 .8 8, 0 .05.

04:10 Here we have 0 ,1, here we have 125 divided by 500, here we have 0 ,01, and here we have 160, 180, 180 ,000 divided by 5, here we have negative 40.

04:31 So here we have that, a is equals to negative 40, further, we have that t plus 125 divided by 500a is equals to 1800 divided by 5...

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