Question

Brother needs help asap:

Refinery mixes high octane and low octane fuel to produce regular and premium gasoline. The profits per gallon of premium gasoline is produced by mixing 1/2 gallon of each of the fuels.
One gallon of regular gasoline is produced by mixing 1/4 gallon of high octane with 3/4 gallon of low octane. If there are 500 gallons of high octane and 600 gallons of low octane available, how many gallons of each gasoline should the refinery make?

Answer 1

if u guys could explain it i'd be really appreciate it. He did all the other ones on the worksheet but the end ones are stumping him. He can read what u guys write so ill pass it on when someone starts helping. Thanks

Answer 2

no i don't have the right answer
do u get it thou?

Answer 3

no problem

Answer 4

@aryandecoolest

Answer 5

can u explain the steps?

Answer 6

is this the answer?
premium gasoline 250 gallons
regular= 125 gallons

Answer 7

foh premium m sure its 250

Answer 8

foh regular its either 125 or 500 m not sure abt the regular thingy

Answer 9

can u explain how to show work/steps because he read it and says he's confused on how u came up with this answer

Answer 10

lemme try

Answer 11

thank u soooo much

Answer 12

do u know what the constraints would be too?

Answer 13

i got it i guess its the ryt ans
500(1/2) +500(1/2)=500
500(1/4) +500(3/4)=500
foh regular and premium it wud be 500 gallons

Answer 14

This is the brother,hey this is linear programing so instead of equals they should be less then or equal to and so on. Also there must be constraints as well.

Answer 15

u have 500 gallon high octane fuel and 600 gallon of low octane fuel....you can only take 500 gallons from each of the fuels
and acc to the question 1/2+1/2=1
therefore 500 (1/2) +500(1/2)=500
and 1/4+3/4=1
500(1/4) +500(3/4)=500

Answer 16

for example there would be 3x +2y<40 you know like that

Answer 17

@midhun.madhu1987

Answer 18

please someone help i am stuck.

Answer 19

Anyone. I would really appreciate the help. I am really stuck on the last two questions.

Answer 20

i am so sorry... no idea...

Answer 21

OK i worked it out and somehow i got this thing....actually this is a good ratio problem where the goal is to use all or as much of the high and low octane as possible to make gasoline.....

Answer 22

For premium gasoline, you have x gallons high octane for x gallons low octane.
For regular gasoline you have y gallons high octane for 3y gallons low octane
so your constraints will be like,
500 gallons of high octane so x+y<=500
600 gallons low octane so x+3y<=600

Answer 23

and subtracting first from second u will get
\[2y \le 100\]
\[y \le 50\]
\[x \le 450\]

Answer 24

now determining the answer is tricky here: suppose you use 450 gallons each of high and low octane for premium gas for 900 gallons premium gas.....
You use 50 gallons of high octane and 150 gallons low octane for 200 gallons regular gas..
@Math2400