Sweet Shop has expanded into healthy smoothies. They use three fruits and a variety of other ingredients to make their smoothies. For simplicity, we are only analyzing their fruit and “end product” requirements. Sweet Shop uses bananas, blueberries and strawberries (N,B and S abbreviations, respectively), and produces “wildFruit”, “RedYellowNBlue” and “BerryMania” smoothies (WF, RYB, BM). Our units are in ‘pounds’, and we assume that fruit weight is additive in the smoothie products: 1 lb of bananas blended with 1 lb. of blueberries and 1 lb of strawberries would result in 3 lbs of smoothie.
For the next production period, we want to purchase fruit such that we produce at least 50 lbs. of each smoothie product.
Suppliers have available 250 lbs of bananas, 100 lbs. of blueberries and 200 lbs. of strawberries. Cost per pound is ($6, $10.5, $8.5) for (N,B,S) respectively. This is the most we can use
On a per pound basis, we sell WF for $12, RYB for $15 and BM for $18.
Each of our smoothie products (in aggregate) have some mix requirements as well as average ORAC (Oxygen Radical Absorbance Capacity) requirements.
wildFruit – cannot be made up of more than 40% of any one kind of fruit. Average ORAC must be at least 1000.
RedYellowNBlue – Must consist of at least 25% of each of the three kinds of fruit. Average ORAC must be at least 1100.
BerryMania – cannot consist of more than 10% bananas, and each of the two other fruits (berries) must be at least 30% of the total amount made. Average ORAC must be at least 1800.
Note that the individual ORAC ratings for bananas are 210, for blueberries 2400 and for strawberries 1540.
Other Constraits:
At least 50% of available fruit must be used.
Individual smoothie products (by weight) cannot exceed 50% of total smoothie production, and be at least 20% of total smoothie production.
Cost Requirements: Banana's and Strawberries come from Freda's Fruits while Blueberries come from Beatrice Farms. A single supplier can have at most 65% of the total fruit expenditures related to the production of smoothies.
Time is not a constraint and is unknown.
Find the optimal way of producing smoothies for Sweet Shop that satisfies all requirements and maximizes profit. Whole numbers (and whole fruit) not required. Solutions must be integers.