H2627 - Math 330 Homework(Pages 156,166,181(Page 156 2...

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Unformatted text preview: Math 330 Homework (Pages 156,166,181) (Page 156 # 2) Determine the production levels needed to satisfy a final demand of 18 units for agriculture but no units for manufacturing or services. Do not compute an inverse ma- trix. The sectors of the economy and their internal production levels are shown below: Manufacturing Agriculture Services Manufacturing 0.1 0.6 0.6 Agriculture 0.3 0.2 0.0 Services 0.3 0.1 0.1 SOLUTION: We let vectorx = x Man x Ag x Ser be the vector of production quotas. Then vectorx must be the sum of the internal production requirements (a linear combination of the columns of the above table) plus the required final demand: vectorx = x Man x Ag x Ser = . 1 0 . 6 0 . 6 . 3 0 . 2 . 3 0 . 1 0 . 1 x Man x Ag x Ser + 18 This gives the following augmented matrix: (Using that vectorx = Cvectorx + vector d so vectorx- Cvectorx = vector d or ( I- C ) vectorx = vector d ) . 9- . 6- . 6- . 3 . 8 18- . 3- . 1 . 9 R 1 ← 10 R 1 9 = ⇒ 1- 2 3- 2 3- 3 10 8 10 18- 3 10- 1 10 9 10 R 2 ,R 3 ← R 2 ,R 3+ 3 R 1 10 = ⇒ 1- 2 3- 2 3 3 5- 1 5 18- 3 10 7 10 R 2 ← 5 R 2 3 = ⇒ 1- 2 3- 2 3 1- 1 3 30 3 10- 7 10 R 3 ← R 3+ 3 R 2 10 = ⇒ 1- 2 3- 2 3 1- 1 3 30 3 5 9 R 3 ← 5 R 3 3 = ⇒ 1- 2 3- 2 3 1- 1 3 30 1 15 R 1 ← R 1+ 2 R 3 3 & R 2 ← R 2+ R 3 3 = ⇒ 1- 2 3 0 10 1 0 35 1 15 R 1 ← R 1+ 2 R 3 3 = ⇒ 1 0 0 100 3 0 1 0 35 0 0 1 15 COMMENT: If we let A =...
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H2627 - Math 330 Homework(Pages 156,166,181(Page 156 2...

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