expect that manufacturing of 1 unit of mining need 5/7 unit of mining, 1/7 unit of production, and 1/7 unit of communication. To produce 1 unit of production needs 3/7 unit of mining, 2/7 unit of manufacturing, and 2/7 unit of communication. To create 1 unit of communication needs 0 units of mining, 1/7 unit of manufacturing, and 6/7 unit of interaction. Find the proportion of the three assets in the closed design.

You are watching: Find the ratios of products a, b, and c using a closed model.

Let x = units of mining, y = systems of manufacturing and z = units of communication. Then you have the complying with 3 equations with 3 unknowns:
Notice the continuous terms on the ideal hand side of the re-written equations are all zero. When this occurs the equations are said to be homogenious and also then tright here is either one solution (the trirvial solution or x = y = z = 0 ) or infinitely many type of services. It turns out thelast is the case.
Note the last line of the rewriten equation: 1/7 y - 1/7z = 0 or y = z. Plugging y = z into the second equation returns 3/7 x - 5/7 z + 2/7 z = or 3/7 x = 3/7 z or x = z so we have infinitely many type of options wbelow x = y = z. For instance let x = y = z = 7 and you will certainly check out all equations are satisfied. Similarly for any kind of set of numbers where x = y = z. Try it for yourself.
What perform you conclude around the proportions? Don"t feel poor I fooled with this for some time. When you obtain to factors, you will certainly see that the determinant of the matrix formed by these equations is 0. Hence no inverse and no distinctive solution. Hope this helps you.

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