### Brain Teasers

# Ice Cream Quandary

Math
Math brain teasers require computations to solve.

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?

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?

### Hint

Daisy may just be a Flavor Engineer, but her intuition is right on!### Answer

Short answer:Daisy is right.

She should up batch size to 86 scoops to give Scott his $25/batch profit.

Long answer:

Cost to Zee's = $12.90/batch or $0.43/scoop

Cost to Customer = $0.90/scoop (WOW! That's more than a 100% mark-up)

BUT:

17 samples cannot be sold.

So a batch is now only 13 scoops

Cost to Customer = $11.70/batch

Zee's loses $1.20 per batch.

So, Daisy is right!

Now, to let's help her convince management to increase the batch size.

To break even: Our cost to make the scoops < Sales dollars from scoops

To make a $25 profit: Our cost to make the scoops + $25 profit < Sales dollars from scoops

Let's make s=the optimal number of scoops in a batch

Our cost to make the scoops is:

$0.43 * s + $0.43 * 17 (because we gave 17 away to marketing)

Sales from the scoops are:

$0.90 *s

Therefore:

$0.43 * s+ $0.43*17 + $25 < $0.90 * s

A little algebra, please:

0.43s+32.31<0.90s

0.47s>32.31

s > 68.75 scoops to sell

Adding in the samples Daisy gave away to Sally:

s = 69 + 17 = 86 scoops/batch

Daisy needs to up the batch size to 86 scoops to ensure a $25 profit per batch.

And, most importantly, she can use her math to convince Sally and Scott to keep making the Purple Pinto!

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## Comments

That one was just way to much work for me.

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

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.

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.

Signmeup are you playing cookie world? This teaser sounds like that game.

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.

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.

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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