Are you studying Linear Programming? Let's see you set it up.
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 $200 million for the petrol division. At what level should each division produce in order to satisfy this demand?
thanks in advanced =D
There may be an alternative in old fashioned simultaneous equations:
Define:
e = electricity produced ($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.
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