C&A makes 5 different flavors of ice cream

Answer:

Let us assume that the machine is first used to make Vanilla ice cream.

After the initial setup time and production time is completed, let us assume that X gallons of vanilla ice cream has been produced.

This X gallons has to satisfy the demands for the subequent setup times of the machine to produce ice creams of other flavours plus the production times of the other four flavours, i.e. (4*45 +4*30) minutes

= (180 + 120) minutes

= 300 minutes

After the other 4 flavours have been produced, the machine would again be used to manufacture vanilla ice cream. During this period of production also, there should be enough inventory of vanilla ice cream to satisfy the demand. Thus an additional setup time and production time for the next batch of vanilla ice cream has to be considered, i.e. (45 + 30) = 75 minutes

Thus the total minutes for which inventory has to be maintained = 300 + 75 minutes

= 375 minutes

= 375/60 hours

= 6.25 hours

Demand for vanilla ice cream per hour = 0.3 gallons

Demand for vanilla ice cream for 6.25 hours = 6.25*0.3 = 1.875 gallons

Thus C&A should produce a minimum of 1.875 gallons of vanilla ice cream per batch.

OPTION B, i.e. 2.8 gallons is thus the correct answer as it would keep the inventory levels for safety stock to a minimum level.