LO$7-2,7-3,7-4,7-6$

Bruno Fruscalzo decided to set up a small production facility in

Sydney to sell to the local restaurants who 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 determined his

demand and setup times, listed in Table $7\mathrm{.}6.$

TABLE $7\mathrm{.}6$

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 $50$ kilograms per hour no

matter which flavor it is producing $($and$,$ of course, it can produce

only one flavor at a time$).$

a$.$ Suppose they operate with a production cycle of $150$ kilograms $(50$

kilograms of fragola, $75$ kilograms of chocolato, and $25$ kilograms

of bacio$).$ What is the capacity of the gelato$-$making process $($in

kilograms per hour$)?$

b$.$ Suppose they operate with a production cycle of $150kgs(50$

kilograms of fragola, $75$ kilograms of chocolato, and $25$ kilograms

of bacio$).$ What is the utilization of the gelato$-$making process?

c$.$ Suppose they operate with a production cycle of $150$ kilograms $(50$

kilograms of fragola, $75$ kilograms of chocolato, and $25$ kilograms

of bacio$).$ What is the average inventory of chocolato?

d$.$ 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 kgs should he produce in each batch?

e$.$ Given your answer to part $($d$),$ how many kgs of fragola should he