In season, trucks full of freshly harvested cranberries arrive at the Fruity Fruit processing plant between 7:00 and 19:00 at the relatively constant rate of 21 per hour. Since a full truck carries 50 barrels (1 barrel = 50kg), this is equivalent to 1050 barrels/hour.

When it arrives in the plant’s yard, the truck empties its load into the fruit dumpers. If those are full, the truck must wait until there is enough free room in the dumpers to empty its load. The dumpers can store up to 3200 barrels. The waiting cost for one truck for one hour is estimated at $75.

The plant processes cranberries at a rate of 600 barrels per hour, beginning at 11:00, until the dumpers are emptied of the deliveries of the day.

 

Recall the Fruity Fruit setting we saw in class. We estimated a total waiting cost for trucks of $60.8K. Suppose now that the plant can add capacity in two possible ways: i. by adding dumper capacity (up to 1000 extra barrels at a cost of $10 000 per 500 barrels). ii. by adding 600 barrels/hour in processing capacity, at a cost of $25 000. Which of the following three options would maximize return on investment (ROI)? 1. adding 500 barrels to the dumper, adding zero barrels/hour to processing capacity. 2. adding 1 000 barrels to the dumper, adding zero barrels/hour to processing capacity. 3. adding zero barrels to the dumper, adding 600 barrels/hour to processing capacity. Note: In this setting, assume that the ROI for a given option equals the savings in waiting costs from the option, divided by its cost. Provide details of your reasoning and calculations for the 3 options. You can refer to the exercise solution in your reasoning. For instance, if one of the components of a calculation equals the area of the triangle in the solution, you can directly refer to the values in the solution for that triangle.