What is the smallest roaster required to roast 75,000 green beans annually at 80% capacity?

To determine the smallest roaster required to roast 75,000 grams of green coffee beans annually at 80% capacity, it's important to first understand the relationship between roaster capacity and annual roasting needs.

First, since 75,000 green beans equate to 75,000 grams (or 75 kilograms), we need to calculate how much capacity would be needed to achieve this while operating at 80% efficiency. If a roaster is operating at 80% capacity, then only 80% of its total capacity is available for roasting beans.

Let’s denote the required capacity of the roaster by x kg. At 80% capacity, the effective roasting output would be 0.8x kg. To meet the annual requirement of 75 kg, we can set up the equation:

0.8x = 75 kg.

To find the necessary capacity of the roaster, we need to solve for x:

x = 75 kg / 0.8 = 93.75 kg.

This means that to meet the annual roasting requirement while running at 80% capacity, the roaster must have a capacity of at least 93.75 kg. Since roasters typically come in standardized sizes, we round up