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OT: Math Question For You Folks

 10-16-2004, 09:29 PM #1 ECL Very slippery slope     Join Date: Feb 2002 Location: Middle America Country: Posts: 79,085 vCash: 500 OT: Math Question For You Folks I'm having major trouble with this Calc question. It's bugging the crap out of me. I have some of the work done but I can't get the equations that I have to plug into the calculator to get the feasible region. I'm hoping one of you guys can help me out on this. Problem: To practive a healthy lifestyle and to maintain his weight at 165 pounds without diety, Darren wants to design a m,onthly exercise program consisting of cycling and running. He would like to exercise at most 14 hours each month, devoting at most 9 hours to cycling and between 4 and 8 hours to running. A Person of Darren's weight burns 422 calories for each hour of cycling and 462 calories for each hour running. How many hours should be allotted to each activity to maximize the number of calories burned each month? Okay. Here's what I have so far: Let x = Cycling Let y = Running Let the objective = Calories Objective equation: Calories = 422x + 462y Constraint Inequalities: x + y (greater than or equal to) 14, x (greater than or equal to) 9, 4 (less than or equal to) y (greater than or equal to) 8, x (greater than or equal to) 0, y (greater than or equal to) 0. I have no idea where to go after that. I'm trying to find the feasible reagion equations (obviously need two of them).
 10-16-2004, 09:38 PM #2 Crease Registered User     Join Date: Jul 2004 Posts: 9,833 vCash: 500 Solve for one of the variables so you have a specific value for X or Y, and then replace the other variable so there is only one letter in your equation. Then solve for that variable algebraicly with respect for the maximum value by performing a CIT test. I can't give you a more detailed explaination because I slept through this class last year. (Senioritis)
10-16-2004, 09:43 PM
#3
ECL
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Quote:
 Originally Posted by Crease29 Solve for one of the variables so you have a specific value for X or Y, and then replace the other variable so there is only one letter in your equation. Then solve for that variable algebraicly with respect for the maximum value by performing a CIT test. I can't give you a more detailed explaination because I slept through this class last year. (Senioritis)
Well, that's not exactly what I'm looking for. I'm trying to find the equations to get to the feasible region (which are two inequality questions). And somehow it should have to involve the alotted hours for each activity and not just the objective equation. The objective is just to take the ends of the feasible region to show the maximum amount of calories he can burn per month.

 10-16-2004, 11:40 PM #4 pld459666 Registered User     Join Date: Feb 2002 Location: Danbury, CT Country: Posts: 17,517 vCash: 500 I think that the best solution is going to be this 8 hours of running at 462 per hour = 3696 6 hours of cycling at 422 per hour = 2532 total calories burned in an 14 hour period is 6228 422(6) + 462(8) I'm horrible at math so I may be the most clueless person to answer this question, but if you are looking to maximize calories burned during a 14 hour period and are limiting hours to 2 different activities, max out your highest calorie per hour output (running per say), 8 hours = 3696 and cycling 6 hours = 2532. 7 & 7 = 6188 calories burned 9 cycling and 5 running = 6108 calories burned Hopefully I didn't confuse the issue more.
 10-17-2004, 12:45 AM #5 ECL Very slippery slope     Join Date: Feb 2002 Location: Middle America Country: Posts: 79,085 vCash: 500 See, I got it up that far. That was more of obvious to me. BUT, I need to know the eqaution to put it into a graphing calculator and graph it. It's an inequality equation I need. It's just the bane of me tonight.
 10-17-2004, 09:48 AM #6 pld459666 Registered User     Join Date: Feb 2002 Location: Danbury, CT Country: Posts: 17,517 vCash: 500 I have my trusty TI-83 Plus at the ready if you need help :lol like I could really be that helpful
 10-17-2004, 01:11 PM #7 Fletch Registered User   Join Date: Feb 2002 Location: Brooklyn Posts: 21,469 vCash: 500 Tell Darren to run more and since he will lose more weight, he should eat some more candy bars to offset that weight loss, thus creating another variable, and that is c, for candy bars.
10-17-2004, 02:10 PM
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AJ1982
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My answers are as follows:

6 hours to cycling

8 hours to running

which is 6228 calories.

I solved the problem by using solver in excel. Solver allows you to use multiple equations (constraints) to solve a problem. It's a very useful technique for supply chain management issues, which can get a bit complicated. It might've been easier to just plug in for this one.

I have attached the excel spread sheet, go to tools and pick Solver to check out how I plugged the constraints into solver. You might have to get an excel toolpack to get that feature though.

I'm not sure how you'd go about getting the inequality equations you want to graph though. I'm not really sure which equations you mean. You have your objective function and your constraints. Constraints give you a range of possibilities and the objective function gives you some number based on those possibilities.

So like you have above,

Obj Function = 422*X+462*Y

then the constraints,

0<X<9
4<Y<8
(422*X+462*Y)<14

All inequalities including equivalency (so ">" is greater than or equal to, and "<" is less than or equal to)

So you see the constraints are your ranges for X and Y, and there is really only one equation, it is simply a bounded equation. I suppose you could use an XYZ graph to graph the problem. The x-axis and y-axis would be simply the hours for X and Y. The z-axis would be the calories and would be calculated by your objective function. You won't be able to graph that on a calculator though, but you could use maple for it.
Attached Files
 problem.zip‎ (1.6 KB, 2 views)

Last edited by AJ1982: 10-17-2004 at 02:36 PM.

 10-17-2004, 07:38 PM #9 Edge Registered User     Join Date: Mar 2002 Location: Sin City Country: Posts: 13,196 vCash: 500 This is exactly why I got my bachelors degree in something that was reading/writing intensive and not number oriented. Sheesh I'll be graduated law school in two months and people say I'm crazy for the stuff i have to research and study. I'd have shot myself by now as a math person.
10-17-2004, 08:38 PM
#10
AG9NK35DT8*

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:lol
Quote:
 Originally Posted by Fletch and since he will lose more weight, he should eat some more candy bars to offset that weight loss, thus creating another variable, and that is c, for candy bars.
:lol

awesome, that seems to be a good answer to me.

10-18-2004, 02:04 AM
#11
ECL
Very slippery slope

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Quote:
 Originally Posted by Edge This is exactly why I got my bachelors degree in something that was reading/writing intensive and not number oriented. Sheesh I'll be graduated law school in two months and people say I'm crazy for the stuff i have to research and study. I'd have shot myself by now as a math person.
Well, I'm going for my PHD in Pharmacy. God knows why I need calculus in th elong run.

 10-18-2004, 05:12 AM #12 patnyrnyg Registered User   Join Date: Sep 2004 Posts: 5,487 vCash: 500 I knew a stripper who was doing her undergrad in pharmacy. She was taking Calc-2, which she called "Pharmacy Math". She never became a pharmacist. This was 9 years ago, now she in jeweler school. I am starting my masters in secondary ed math in the summer. I took AP Calc in HS and do not remember ANY of it. Reading this, I remembered these types of questions, but do not have the foggiest idea onhow to solve it. Fortuntately for now, I teach junior high, so no chance of needing this in the near future. I did buy a few calc textbooks on EBay, hoping I could re-teach myself.
10-18-2004, 01:05 PM
#13
Draft Guru
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Quote:
 Originally Posted by patnyrnyg I knew a stripper who was doing her undergrad in pharmacy. She was taking Calc-2, which she called "Pharmacy Math". She never became a pharmacist. This was 9 years ago, now she in jeweler school. I am starting my masters in secondary ed math in the summer. I took AP Calc in HS and do not remember ANY of it. Reading this, I remembered these types of questions, but do not have the foggiest idea onhow to solve it. Fortuntately for now, I teach junior high, so no chance of needing this in the near future. I did buy a few calc textbooks on EBay, hoping I could re-teach myself.

Where do you teach?

 10-18-2004, 03:47 PM #14 patnyrnyg Registered User   Join Date: Sep 2004 Posts: 5,487 vCash: 500 In NYC, and Junior High to High School transfers rarely happen, unless the HS in question is in desperate need. However, the only HS's in desperate need are the schools at which no one wants to teach, and wouldn't likely offer calculus. Besides, math is a shortage area in junior high so they would never let me create a junior high vacancy to fill a HS vacancy.

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