# Stunned by my finite mathematics question

• Jul 4th 2011, 06:07 AM
jc90
Stunned by my finite mathematics question
Im studying finite maths right now, and i came across this question which is rather difficult...i would like some help in solving this question

A manufacturer has three divisions, which produce electricity, steel and petrol. To produce \$1 of electricity, the division needs \$0.02 worth of electricity, \$0.20 worth of steel and \$0.10 worth of petrol. To produce \$1 of steel, the division needs \$0.02 worth of electricity, \$0.01 worth of steel and \$0.02 worth of petrol. To produce \$1 of petrol, the division needs \$0.10 worth of electricity, \$0.01 worth of petrol. The manufacturer estimates the sales demand to be \$300 million for the electricity division, \$100 million for the steel division and \$200 million for the petrol division. At what level should each division produce in order to satisfy this demand?

• Jul 4th 2011, 07:51 AM
TKHunny
Re: Stunned by my finite mathematics question
Are you studying Linear Programming? Let's see you set it up.
• Jul 5th 2011, 09:40 AM
SpringFan25
Re: Stunned by my finite mathematics question
There may be an alternative in old fashioned simultaneous equations:

Define:
e = electricity produced (\$m)
s = petrol produced (\$m)
s = petrol produced (\$m).

The production of each must satisfy the external market demand and also the demand from the other divisions. So for electrcity this would be:

300 (external)
0.02e (demand from electric division for electricity)
0.1p (demand from petrol division for electricity)
0.02s (demand from steel division for electricity)

so (and similarly for the other divisions):
e=300 + 0.02e + 0.1p + 0.02s
s=100 + 0.2e + 0.01s
p=200 + 0.1e + 0.02s + 0.01p

That is 3 equations in 3 unknowns, solve using your preferred method.
• Jul 6th 2011, 05:22 AM
jc90
Re: Stunned by my finite mathematics question
well my lecturer said i could solve it using gauss-jordan elimination method, but when i tried, i got answers with a lot of decimals..which looked wrong

could you elaborate further please =D

thanks
• Jul 6th 2011, 05:41 AM
HallsofIvy
Re: Stunned by my finite mathematics question
It would be better if you showed how you tried to solve those equations.
• Jul 6th 2011, 05:56 AM
jc90
Re: Stunned by my finite mathematics question
lets say, electricity = x , steel = y , petrol = z
then,

\$1 electricity=0.02x + 0.20y + 0.10z

\$1 steel = 0.02x + 0.01y + 0.02z

\$1 petrol = 0.10x + 0.01z

i multiplied the LHS to meet the demand level, say,
\$1 electricity x 300 mil
\$1 steel x 100mil
\$1 petrol x 200mil

then,
300000000 = 6000000x + 60000000y + 30000000
100000000 = 2000000x + 1000000y + 2000000z
200000000 = 20000000x + 2000000z

after that, i solved those equations simultaneously, i get

x = 550/131
y = -3200/131
z = 7600/131

HELP, im lost