Bruno decided to set up a small production facility in Sydney to sell to local restaurants that want to offer gelato on their dessert menu. To start simple, he would offer only three flavors of gelato: fragola (strawberry), Chocolato (chocolate), and bacio (chocolate with hazelnut). After a short time he found his demand and setup times to be
Fragola Chocolato Bacio
Demand (kg/hour) 10 15 5
Setup time (hours) 3/4 1/2 1/6
Bruno first produces a batch of fragola, then a batch of chocolato, then a batch of bacio and then he repeats that sequence. For example, after producing bacio and before producing fragola, he needs 45 minutes to set up the ice cream machine, but he needs only 10 minutes to switch from chocolato to bacio. When running, his ice cream machine produces at the rate of 50 kg per hour no matter which flavor it is producing ( and, of course, it can produce only on flavor at a time).
a. Suppose Bruno wants to minimize the amount of each flavor produced at one time while still satisfying the demand for each of the flavors. (He can choose a different quantity for each flavor.) If we define a batch to be the quantity produced in a single run of each flavor, how many kilograms should he produce in each batch?
b. Given your answer in part (a), how many kilograms of fragola should he make with each batch?
c. Given your answer in part (a), what is the maximum inventory of chocolato? (assume production and demand occur at constant rates)