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Hey WSR
I am in the business of selling baked goods. I have two products. The 'ingregients' of products we will assign as A, B and C. The product being D.
There are two different scenarios, the first we sell sliced cake the second we sell whole cakes. We are not a baked goods store, we are baked goods manufacturer for a well known brand so we have no issues with selling our product regardless of our output.
I am trying to find which will net more product, using the least ingredients.
Sliced cake is made using 2oz of Ingredient A, 2oz of Ingredient B, and 1 oz of Ingredient C. We retail each slice for 7$.
Whole Cakes are made using 10oz of Ingredient A, 10oz of Ingredient B, and 7oz of Ingredient C. We retail each cake for 30$
Now (magically) every 5th product made between 1-10 extra of that product appears. Assume there is an equal chance of the extra product being between 1-10.
Marketing dept is telling us we have equal market interest in both products, suddenly our main warehouse has a fire, and we are left with a shortage of ingredients. currently we have 1500 of Ingredient A & B, and 1050 of Ingredient C. If the company is allocating these ingredients baking Sliced cakes, or Whole cakes which will net the company more money, while maintaining the most efficiency of ingredient use?
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>>343417
You said nothing abot the ingredients having different values.
equal chance of being between 1-10 extra means estimated value is 5 extra for every 5th- in other words doubling of amount.
Since A B and C have same value we can go by the pure numbers.
For sliced you for C need half the amount of A or B, in other words A/B will be the limiting factor, some of C will remain (750 would be enough for using all 1500 of A/B) So for sliced you can make 1500/2 = 750 slices, doubled that means 1500, $7 for each means $10500.
For whole cakes you need 7/10 for C of A/B, that is very close to 2/3, whch means the amount would be used optimally since you have about 2/3 of C compared to A/B left.
1500/10 per cake means 150 cakes, doubled that makes 300. At $30 per cake that makes $9000
-->Sliced is better but Whole is more efficient in ingredient use.
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