An engineering department charges 25% of its total monthly costs to the computer department. The computer department charges 20% of its costs to the engineering department.
Total monthly cost of Eng dept. is $x and comp dept is $y
At any given month the eng dept cost, not including what it pays to comp dept is $95k. And the comp dept cost not including what is paid to eng dept is $85500.
1) write equation for x and y
2) determine matrix A in the equation x=d + Ax
3) calculate the total monthly cost for each dept.
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1) equations i've come up with for total cost to each department are: a) x = 0.2y + 95000 ; b) y = 0.25x + 85500
2) matrix A I am saying is ...
3) I believe this to be a open Leontief economic modeling question based on the x=Ax+d part in 2)
or x = (I-A)-1x * d
(I-A) is Identity matrix minus A which gives
det of (I-A) is 1/0.95
(I-A)-1 . is
multiplying this by the 2x1 matrix of
gives x = 110556.25 or just $110,556
and y = $99275
________________________________
would appreciate if anyone could let me know am I on the right track, if not, where I'm going wrong. Cheers.
Total monthly cost of Eng dept. is $x and comp dept is $y
At any given month the eng dept cost, not including what it pays to comp dept is $95k. And the comp dept cost not including what is paid to eng dept is $85500.
1) write equation for x and y
2) determine matrix A in the equation x=d + Ax
3) calculate the total monthly cost for each dept.
_____________________________________________________________________________________________________________________________________________
1) equations i've come up with for total cost to each department are: a) x = 0.2y + 95000 ; b) y = 0.25x + 85500
2) matrix A I am saying is ...
0 | 0.2 |
0.25 | 0 |
3) I believe this to be a open Leontief economic modeling question based on the x=Ax+d part in 2)
or x = (I-A)-1x * d
(I-A) is Identity matrix minus A which gives
1 | -0.2 |
-0.25 | 1 |
det of (I-A) is 1/0.95
(I-A)-1 . is
0.95 | 0.2375 |
0.19 | 0.95 |
multiplying this by the 2x1 matrix of
95000 |
85500 |
gives x = 110556.25 or just $110,556
and y = $99275
________________________________
would appreciate if anyone could let me know am I on the right track, if not, where I'm going wrong. Cheers.