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Ice Cream Quandary

Math brain teasers require computations to solve.


Puzzle ID:#26432
Fun:*** (2.69)
Difficulty:*** (2.24)
Submitted By:signmeup74*pl******
Corrected By:signmeup74




Zee's Ice Cream Shop is world renowned for making new and inventive ice cream flavors from scratch. They've made great profits on their Marshmallow Mustang and Cinnebago flavors, but their Purple Pinto is just not turning a profit!
Scott, Zee's President, says that customers just don't want to eat purple ice cream. He thinks they should pull the flavor and move on. However Sally, Zee's Marketing Director, disagrees. She has taste tested the flavor with a sampling poll and it got rave reviews.
Daisy, the lowly Flavor Engineer, loves the Purple Pinto and knows that it has profit potential! She thinks the problem might be stemming from the small batch sizes and the fact that Sally takes scoops for sample polls every time they run a batch of the flavor.
Daisy has collected the following information:
1. Currently, there are 30 scoops in a batch.
2. It costs Zee's $12.90 to make each batch, right now.
3. A scoop sells for $0.90.
4. A small profit is not enough! Scott wants $25 per batch to make up for lost time.
5. Sally will not stop taking 17 sample scoops per batch.
First of all, is Daisy right? Or is the Purple Pinto just doomed?
If she is, can you help Daisy determine how large batches should be to ensure that Zee's makes a profit and keeps making her favorite flavor?

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Oct 19, 2005

That one was just way to much work for me.
Oct 25, 2005

Oh good I am not first another great one signmeup. A lot of thinking and writing, but got most of it and then
Oct 30, 2005

I disagree with your answer. 69 is the number of scoops she needs to sell not the batch size! The batch size would have to be 86 to allow for the 17 sample scoops. Here is the math:

Costs: 86 * $0.43 = $36.98
Sales: 69 * $0.90 = $62.10
Profit: $62.10 - $36.98 = $25.12

Other than that oversight I liked the teaser.
Nov 25, 2005

Signmeup are you playing cookie world? This teaser sounds like that game.
Jan 27, 2009

I got the same answer but with somewhat simpler math.

Cost per scoop is 12.90 / 30 = .43. Profit needed is 25 + 17 x .43 = 32.31 divided by the .90 - .43 = .47 profit per scoop = 68.7 scoops sold plus 17 samples = 85.7 scoops.

No algebra needed.

Apr 16, 2009

Would be much easier if Scott would just fire dumb sh*t Sally who currently gives away over half of the batch.

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