Question

A fishing fleet delivers fresh fish to a cannery factory, where the fish is canned. Suppose that daily input to the cannery follows the following pattern: (1) 100 tons/hr. between 8 a.m. and 12 noon, (2) 75 tons/hr. between 1 p.m. and 3 p.m., and (3) 100 tons/hr. between 3 p.m. and 5 p.m. Note that there is no input between 12 noon and 1 p.m. The processing capacity of the cannery is: (1) 100 tons/hr. between 8 a.m. and 11 a.m., (2) 50 tons/hr. between 11 a.m. and 2 p.m., and (3) 100 tons/hr. between 2 p.m. and 5 p.m. Assume that there is unlimited freezer space for unprocessed fish.

a. Draw an inventory buildup diagram that shows inventory of unprocessed fish in the freezer starting at 8 a.m. and ending at 5 p.m.
b. Consider a fish that enters the cannery between 8 a.m. and 12 at noon. What is the average time (in minutes) spent by such a fish in the freezer before being packed?

Answer 1

a. The inventory buildup diagram shows the inventory of unprocessed fish in the freezer from 8 a.m. to 5 p.m. b. The average time spent by a fish in the freezer before being packed is 100 minutes.

Step-by-step explanation:

a. To draw an inventory buildup diagram, we need to calculate the net input and output of fish at each hour for the time period from 8 a.m. to 5 p.m. We can then plot these values on a graph to visualize the inventory buildup. Here is the calculation:

From 8 a.m. to 12 noon, the net input is 100 tons/hr. From 8 a.m. to 11 a.m., the net output is 100 tons/hr. Therefore, the inventory buildup is 100 tons/hr.

From 12 p.m. to 1 p.m., there is no input or output. Therefore, the inventory buildup remains the same.

From 1 p.m. to 3 p.m., the net input is 75 tons/hr. From 1 p.m. to 2 p.m., the net output is 50 tons/hr. Therefore, the inventory buildup is 75-50 = 25 tons/hr.

From 3 p.m. to 5 p.m., the net input is 100 tons/hr. From 3 p.m. to 5 p.m., the net output is 100 tons/hr. Therefore, the inventory buildup is 0 tons/hr.

b. A fish that enters the cannery between 8 a.m. and 12 noon will spend an average time in the freezer of (Inventory buildup) / (Net input per hour) minutes. From the inventory buildup diagram, we know that the inventory buildup during this time period is 100 tons/hr.

The net input per hour is also 100 tons/hr. Therefore, the average time spent by a fish in the freezer before being packed is 100 minutes.