" Johnny is commercially making juice by combining apples, oranges, and pears..."

[MarcB]

" Johnny is commercially making juice by combining apples, oranges, and pears..."

Hey there.

This is a real life problem I'm trying to solve. I've spent a couple of hours pondering it but I don't really know where to start. I know someone out there can probably whip through this problem, and I would really appreciate some help. I've tried really hard to articulate the problem, but if you have any questions or there's something I've left out, I'd be happy to clarify anything.

Problem

Johnny is commercially making juice by combining apples, oranges, and pears. At the start of today, Johnny has 1400 oranges, 800 apples, and 200 pears to prep for juicing, and needs them all to be finished being prepped at the same time.

Johnny has 25 workers in total

Team A has 13 workers and can prep oranges and apples but not pears
Team B has 7 workers and can prep apples and pears but not oranges
Team C has 5 workers and can only prep apples

Oranges take 1.5 times longer to prep than apples and pears take 1.2 times longer to prep than apples.

Workers can alternate working between fruits in their skillset without losing productivity eg. a Team A worker can prep orange, apple, orange, apple, orange, or just apples, or just oranges.

Not all workers in a team have to complete the same tasks eg. one Team A worker can be assigned to just prep oranges, one Team A worker can just assigned to just prep apples, and another Team A worker could alternate fruits in their skillset as explained above.

Solve to decide how Team A, B, and C should operate so that all oranges, apples, and pears are finished being prepped at the same time. Is it possible to solve in a way to where Johnny can make team assignment decisions based on how many oranges, apples, and pears need to be done at the beginning of the day?

Thanks in advance!

-Marc

 

[MarcB]

Hey Dennis

Yes, all of your statements are correct. My end goal here would be to have an equation or set of equations that could solve this problem if the number of workers in Team A, B, or C changed, or if the number of oranges, apples, and pears were different on any given day. It's like a workforce management problem. Thanks heaps for your help!

 

[stapel]

This is a real life problem I'm trying to solve.

Well, it's kind-of similar to something that might happen in "real life", but real life has soooooo many other considerations. :shock:

I've spent a couple of hours pondering it but I don't really know where to start.

A good place to start would be with the method(s) you know for this sort of exercise. Are you familiar with solving systems of equations? Have you studied optimization techniques? And so forth. (Whatever has been covered recently in class is likely to be a big hint as to how you're expected to proceed.)

I know someone out there can probably whip through this problem...

Of course! But this forum exists so that the volunteers (who give of their time and experience when and as they're able) can help struggling students do this on their own. So we'll need you to work with us on this.

Johnny is commercially making juice by combining apples, oranges, and pears. At the start of today, Johnny has 1400 oranges, 800 apples, and 200 pears to prep for juicing, and needs them all to be finished being prepped at the same time.

Johnny has 25 workers in total

Team A has 13 workers and can prep oranges and apples but not pears
Team B has 7 workers and can prep apples and pears but not oranges
Team C has 5 workers and can only prep apples

Oranges take 1.5 times longer to prep than apples and pears take 1.2 times longer to prep than apples.

Workers can alternate working between fruits in their skillset without losing productivity eg. a Team A worker can prep orange, apple, orange, apple, orange, or just apples, or just oranges.

Not all workers in a team have to complete the same tasks eg. one Team A worker can be assigned to just prep oranges, one Team A worker can just assigned to just prep apples, and another Team A worker could alternate fruits in their skillset as explained above.

Solve to decide how Team A, B, and C should operate so that all oranges, apples, and pears are finished being prepped at the same time. Is it possible to solve in a way to where Johnny can make team assignment decisions based on how many oranges, apples, and pears need to be done at the beginning of the day?

This sounds more like an optimization-techniques exercise (that is, from a class possibly long after calculus). What class are you taking, that generated this? What's your math background? (Love it, or not so fond? Loads of current experience, or it's been ten years between high-school and now?)

When you reply, please provide a clear listing of your thoughts and efforts so far. Thank you!