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?

thanks in advanced =D

Re: Stunned by my finite mathematics question

Are you studying Linear Programming? Let's see you set it up.

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.

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

Re: Stunned by my finite mathematics question

It would be better if **you** showed how you tried to solve those equations.

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