Zee’s Ice Cream Shop is famous the world over for making new and inventive ice cream flavours from scratch. They’ve made great profits on their Marshmallow Mustang and Cinnebago flavours, 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 flavour and move on. However Sally, Zee’s Marketing Director, disagrees. She has tested the flavour with a sampling poll and it got rave reviews.
Daisy, the lowly Flavour 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 flavour.
Daisy has collected the following information:
- Currently, there are 30 scoops in a batch.
- It costs Zee’s $12.90 to make each batch, right now.
- A scoop sells for $0.90.
- A small profit is not enough! Scott wants $25 per batch to make up for lost time.
- 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 favourite flavour?
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, 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 Maths to convince Sally and Scott in order to keep making the Purple Pinto!
