Any math professors or linear programming,I need some help in Industrial Design Class

kycarguy 935 · 05-01-2009, 07:46 PM

Hi guys.

I am stuck on a problem in my Industrial Design class. This is the last problem of the semester and I am getting frustrated. I know there are people on here with every area of expertise.

The book is pretty useless.

Can anyone help? Please.......Thanks in advance.

I will post the problem.

1. The following data are for a company that produces washers and dryers.
• Dryers retail for $198 and contribute $15 to profit.
• Washers retail for $499.95 and contribute $45 for profit.

• The washer blade is limited in production capacity to 50 blades, while all other components have no limits.

• Chassis assembly requires 6 person-hours for each dryer set and 18 person-hours for each washer. The plant employs 225 workers for an 8-hour shift to perform chassis assembly operations.

• A dryer requires 1 person-hour on the assembly line, a washer set 1.6 person-hours. There are 30 people on a single 8-hour shift assigned to assembly.

• Final inspection requires 0.5 person-hour for the dryer and 2.0 person-hours for the washer. The plant employs 20 full-time inspectors and one part-time employee for 2 hours per day.

a. Write a linear programming model.

b. What is the optimum number of dryers and washers?

c. Calculate the maximum profit.

d. The linear programming and break-even approaches are used to find the selling price for both the dryer and washer, based on $10,000 fixed cost for both dryer and washer with a variable cost of $160 for the dryer and $330 for the washer. Determine how many days will be required until the company starts making a profit for the washers and dryers. Use $198 and $500 as selling prices for the dryer and the washer, respectively.

stomachmonkey · 05-01-2009, 08:29 PM

Neighbors were out drinkin when I got home.

Joinrd em.

No dinner.

6-7 glasses of vino.

I'm useless.

Bump.

kycarguy 935 · 05-01-2009, 08:32 PM

haha Cheers.

Thanks anyway.

John Rogers · 05-01-2009, 08:47 PM

If it were me I would want more information:

- Is the 50 blade limit per day or week or what?

- What is the cost per hour of the assembly people?

- What is the cost per hour of the QA people?

- How many hours per day does everyone work, 8 maximum?

- Are the washers and dryers done on a moving line or does one person do the whole washer or dryer?

This is from working on software the past 4 years that figured manufacturing cost or repair cost for "parts" and in our case it was aircraft components repairs. To figure the cost of doing the work some of the above items were required. If you calculate just by figuring the "hands on" time or when someone is wworking on it the washers take 21.6 total hours and figuring $455 cost to make that amounts to cost per hour of $21.06. For the dryers, they take 7.5 hours and their cost is $183 or $24.4 cost per hour. Both of these ignore the personnel costs associated with the manufacture of the product so it cost less per hour to make washers but the dryers take 1/3 the time and you also have the 50 blade limit which if per day which means you can make 50 washers max per day and that lets you have the time to build 150 dryer per day.

I also forgot to add in things like lost personel time due to vacation, etc but programs usually never figure that in for some reason.

kycarguy 935 · 05-01-2009, 09:14 PM

Thanks John. That helps me understand it much better.

The only information they gave us is posted. I found this same question in the book but no solution to double check answers.

I believe from other problems is an 8 hour maximum work day.

Not sure on the QA people or cost per hour on the assemblers.

The 50 blade limit is a day.

Thanks much.

ChkbookMechanic · ChkbookMechanic's Garage

You don't need anymore than what was listed in the problem to solve.

The first step in linear programming is to create the equations that represent the given constraints(# of washers and driers that can be made in a day, time to make washer or dryer, time to inspect washer and dryer, etc.) and objective (maximize profit).

This site has some sample formulations that could be helpful: http://www.sonoma.edu/users/w/wilsonst/Courses/Math_131/lp/Farm.html

fireant911 · 05-02-2009, 05:50 AM

kycarguy 935,
ChkbookMechanic is indeed correct about setting up the contraint equations. I realize that your assignment is to, in part, write the linear programming model; however, EXCEL has the little-used capability of setting up and solving some rather complex linear programming models. This feature is called Solver. The instructions accompanying this feature are, in my opinion, inadequate yet it is a pretty robust tool. If nothing else, it can serve as a mechanism to set up your constraints (which is essentially the most important part of the assignment). This Solver can handle 100 constraints therefore your assignment can be easy mastered and a solution found.

As a side note, I taught Cost Analysis at the university and I always incorporated EXCEL's Solver as part of the class - in my opinion, it is EXCEL's best kept secret. If interested, I can send you a problem that I used in class along with a detailed walkthrough of setting up this same problem.

kycarguy 935 · 05-02-2009, 09:48 AM

Thanks john,Chkbook and Daryl.

Daryl, I would appreciate if you could send me that problem that you used in class. It would be much appreciated.

Thanks guys.

fireant911 · 05-02-2009, 03:56 PM

Quote:

Originally Posted by kycarguy 935

Thanks john,Chkbook and Daryl.

Daryl, I would appreciate if you could send me that problem that you used in class. It would be much appreciated.

Thanks guys.

kycarguy 935,
The information has been sent to your yahoo E-mail account.

kycarguy 935 · 05-02-2009, 07:41 PM

I received it Daryl and sent a return email. Thanks much. I will be spending some time on it tomorrow to get it worked out.

Thanks again all.

plain fan · 05-03-2009, 07:09 AM

kycarguy935,
Have you worked it through? It's been a few years since using LP but everyone is correct so far. You set up the equations for each constraint then solve with LP. Are you using a packaged software like LINDO/LINGO? I second the suggestion for Excel's sovler functionality. Once you get the formulas you can set it up in a matrix and use linear algebra to solve if necessary.

kycarguy 935 · 05-03-2009, 01:07 PM

Hi Grady,

I haven't worked through it yet. I don't have software to use with this except Excel. This is the first math type problem in the class and from the email the instructor sent everyone is getting stuck.

It has been a few years since I have had this type of math so I will be working on it this evening.

Thanks.