Freshly

Freshly is a local business that sells bottled fresh coconut water and fresh orange juice to local groceries on a daily basis.

Although it takes only about 54 seconds to process one coconut and about 30 seconds to process one kilogram of oranges, Freshly operates for only three hours every morning because they have to ship the bottled products to the market by 8:00 AM. Another important fact is that Freshly has only one piece of equipment to process both coconuts and oranges, so they must process them sequentially.

 
 

On average, one coconut yields 450 ml of coconut water, and one kilogram of oranges yields 520 ml of orange juice. In addition, Freshly must ship at least 30 bottles of orange juice and at most 100 bottles in total every day. These are all 500 ml bottles.

Freshly's profit is 0.85 dollars per liter of coconut water (i.e., \(0.85 \cdot 0.450 = 0.3825\) dollars per coconut) and 0.78 dollars per liter of orange juice (i.e., \(0.78 \cdot 0.520 = 0.4056\) dollars per kilogram of orange).

The goal is to prescribe how many coconuts and how many kilograms of oranges Freshly should process daily to maximize their total profit.