7. (20 points) A company produces two items, but uses up some of each product in

Question

7. (20 points) A company produces two items, but uses up some of each product in the production process, as described by the input-output matrix 6 .2 3 .6 (a) If we produce 100 units of each product, how much is used up in the production process? (b) If we produce 100 units of each product, how much do we actually end up with? (c) How many units of each product should be produced in order to end up with 100 units of each product? i. To solve this problem, you will need the inverse of one of the following matrices. Circle the one that makes sense. 4 .8 4 .8 3 .6 4 .2 3 4 6 2 .4

Explanation / Answer

(a)

on using 100 of each product x1 and x2,

output = 0.6*100x1 + 0.2*100x2 and 0.3*100x1 + 0.6*100x2 =  0.9*100x1 + 0.8*100x2 = 90x1 + 80x2

so 90 units of x1 and 80 units of x2 are used.

(b)

80 + 90 = 170

(c)

0.6x1 + 0.2x2 = 100

0.3x1 + 0.6x2 = 100

x1 =133.33 , x2 = 100

first one.

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