Let a tank costs x $US, a heat exchanger costs y $US, and a vertical separator costs z $US. Then
3x+4y+2z=1575002x+y+3z=900005x+3y+2z=149500 Then
A=⎝⎛32541323215750090000149500⎠⎞ Divide row 1 by 3 (R1=3R1)
⎝⎛1254/3132/3325250090000149500⎠⎞ Subtract row 1 multiplied by 2 from row 2 (R2=R2−(2)R1)
⎝⎛1054/3−5/332/35/3252500−15000149500⎠⎞ Subtract row 1 multiplied by 5 from row 3 (R3=R3−(5)R1)
⎝⎛1004/3−5/3−11/32/35/3−4/352500−15000−113000⎠⎞ Multiply row 2 by −53 (R2=(−53)R2)
⎝⎛1004/31−11/32/3−1−4/3525009000−113000⎠⎞ Subtract row 2 multiplied by 34 from row 1 (R1=R1−(34)R2)
⎝⎛10001−11/32−1−4/3405009000−113000⎠⎞ Add row 2 multiplied by 311 to row 3 (R3=R3+(311)R2)
⎝⎛1000102−1−5405009000−80000⎠⎞ Divide row 3 by −5 (R3=−5R3)
⎝⎛1000102−1140500900016000⎠⎞ Subtract row 3 multiplied by 2 from row 1 (R1=R1−(2)R3)
⎝⎛1000100−118500900016000⎠⎞ Add row 3 to row 2 (R2=R2+R3)
⎝⎛10001000185002500016000⎠⎞A tank costs 8500 $US, a heat exchanger costs 25000 $US, and a vertical separator costs 16000 $US.
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