math problem help

[jai6638]

hey needed some help in this algebra 2 problem that i foud in a textbook :

You are planning a dinner of printo beans and brown rice. you want to consume at least 2100 calories and 44 grams of protein per day, but no more than 2400 milligrams of sodium and 73 grams of fat. So far today, you have confusmed 1600 calories, 24 grams of protein, 2370 milligrams of sodium and 65 grams of fat. Printo beans cost $.57 per cup and brown rice costs $.78 per cup. How many cups of printo beans and brown rice should u make to minimize cost while satisfying your nutiritional requirements??

a table is provided along with the sum:

Contents 1 cup 1cup brown rice ( with salt )

Calories 265 230
Protein ( g) 15 5
Sodium ( mg) 3 10
Fat ( g) 1 1

Any help with this problem would be appreciated .....

 

[five40]

printo beans? Sound dangerous to me.

 

[Yossarian]

it's a trick question. you're on the atkins diet so the answer is to have 2 lbs of bacon wrapped in cheese.

 

[jai6638]

huh?

 

[maziwanka]

Originally posted by: Yossarian
it's a trick question. you're on the atkins diet so the answer is to have 2 lbs of bacon wrapped in cheese.

hahahaha. you've confused him

 

[jai6638]

well im serious and am hoping i could get an answer ...

 

[Hankerton]

What exactly is 1 cup 1 cup?

 

[jai6638]

oh damn..i tried making a table but i gues the format is messed up ...

the columns are

1) contents
2) 1cup
3) 1cup brown rice ( with salt )

 

[dmw16]

Man, math has gotten stupid since I left HS.

 

[BlueWeasel]

Well, you know you need at least 500 more calories and 20g protein, but you can't have more than 30mg sodium and 8g fat.

Based on the data in the table, it would seem to me that 2 cups printo beans only would be the most economical. But if you went with a combination of beans and rice, it would take one cup of beans and two cups of rice to get your calories over 2100.

 

[jai6638]

Well, you know you need at least 500 more calories and 20g protein, but you can't have more than 30mg sodium and 8g fat.

hey... thanks for ur reply.... made inqualities based on that but didnt get the answer.. my answers are in decimals for some odd reason.. how did u get that answer??

 

[BlueWeasel]

Assuming I understood the problem (it's kinda confusing, especially the table):

Well, you know you need the following:
500 calories
20 g protein

And you can't have more than 30mg sodium, or 8g fat.

So, if you went with 2 cups of beans only:
530 calories
30g protein
6mg sodium
2g fat

1 cup beans + 2 cups rice
725 calories
25g protein
23mg sodium
3g fat

If you go with 3 cups of rice only, then you don't get the protein you need and it pushes your sodium to the max:
15g protein (you need 20g)
30mg sodium (30mg sodium is the max)

 

[jai6638]

i see... need to find a way to graph that coz apparently in the examples in the chapter they've graphed it and made use of inequalities... thanks .. ill see if i can graph it ..

 

[oboeguy]

Holy @#$%! They do Linear Programming in Algebra II now? Dude, some of my college juniors have trouble with this on the first day (granted, you have a fairly simple problem). Yes, you have a two variable problem (how much rice, how much bean) so it should be easy to sketch a two-dimensional graph. You should have one linear inequality per nutrient, so it shouldn't take a ridiculous amount of time. Good luck, kiddo. 🙂

BTW, your table sucks.😕

 

[jai6638]

yup they've introduced linear programming for some odd reason.. graphing is not my strong point.. i've got 4 inequalities to graph and after graphing it im getting answers in decimals which doesnt seem right to me..

what are those "college juniors" majoring in ?

 

[oboeguy]

Originally posted by: jai6638
yup they've introduced linear programming for some odd reason.. graphing is not my strong point.. i've got 4 inequalities to graph and after graphing it im getting answers in decimals which doesnt seem right to me..

what are those "college juniors" majoring in ?

Operations Research... which is in part based on Linear Programming! :Q Anyhow, I do not mean to exaggerate, as they do get it quickly enough. My point is that it's challenging enough for serious students at the college level that I can't believe it's being done in Algebra II. Not that I mind, seeing as it's my field and all. 🙂 It's pretty cool to see it taught so early, but I can't imagine you can do much more than graphical solutions of 2D problems with the amount of Math you know at this stage.

 

[desteffy]

try the simplex method :thumbsup:

 

[TranceNation]

the problem statement is not geeky enough for anybody on AT to care about...

 

[Chronoshock]

Haha I did linear programming sophomore year of HS. So just write up your system of eqns bounding it in the different directions. Let rice be x and beans be y or something and then create constraint lines based on that (bounding off the top/right due to max fat/sodium and bounding off the bottom/left due to min calories/protein). Shouldn't be too hard

 

[jai6638]

Originally posted by: Chronoshock
Haha I did linear programming sophomore year of HS. So just write up your system of eqns bounding it in the different directions. Let rice be x and beans be y or something and then create constraint lines based on that (bounding off the top/right due to max fat/sodium and bounding off the bottom/left due to min calories/protein). Shouldn't be too hard

i did exactly what uve stated above.. but somehow my graph looks really messy...do u think getting decimals is alright ??? personally, i think getting decimals is an indicator that ive screwed up somewhere...

Operations Research... which is in part based on Linear Programming! Anyhow, I do not mean to exaggerate, as they do get it quickly enough. My point is that it's challenging enough for serious students at the college level that I can't believe it's being done in Algebra II. Not that I mind, seeing as it's my field and all. It's pretty cool to see it taught so early, but I can't imagine you can do much more than graphical solutions of 2D problems with the amount of Math you know at this stage

we'll be doing a few 3d probs too .... but neways Linear programming is the only thing thats got me thinking so far.... else its beeen a breeze... have been getting a+ in all my tests .. LOL...

btw the following are the constraints i got :

265b + 230 r >= 500 which when simplified gives 53b + 46r >= 100
15b + 5 r >= 20
3b + 10r <= 30
1b + 1r <= 8

are the constraints correct? if not, please advise..

i then graphed the constraints.... and took the points and plugged each of them into the following cost equation:

C=.57b + .78r

so for example.. if the points were (0,100 )

it would be C = .57 ( 0 ) + .78 ( 100 )
= 78