Question
A World Series provider of malts and shakes, has expanded into healthy smoothies at the same time they have moved downtown near TD Ameritrade. They
A World Series provider of malts and shakes, has expanded into healthy smoothies at the same time they have moved downtown near TD Ameritrade. 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. The company 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. We can produce more - plenty of freezer space exists at the new downtown store.
Our 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.
Using EXCEL SOLVER, find the optimal way of producing smoothies for the company that satisfies all requirements and maximizes profit. Whole numbers (and whole fruit) not required.
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