Consider the previous problem with the following changes. Assume the crafter employs a teenage

babysitter to stay with her kids during the show. The babysitter periodically calls the crafter's cell

phone with some problem$/$question$.$ The time between calls is exponentially distributed with a

mean of $15$ minutes. Being a concerned parent, anytime she gets a call from the babysitter, the

crafter will interrupt her conversation with a customer $($if one is present$)$ to handle the call. This

takes her an exponentially distributed amount of time with a mean of $1$ minute. All other aspects

of the problem are the same as in problem $1.$

a$.$ Assuming the crafter is interested in learning such things as the expected number of customers

in the booth and the rate at which customers balk, develop a model for this system. Be sure to

define the states of the system, list the system events, and give the state transition rate diagram.

b$.$ What is the throughput rate for this model?

c$.$ The crafter sells $3$ different items: Victorian Tussie$-$Mussies, dried floral wreaths, and hydrangea

baskets for $$12,$$$45,$ and $$20,$ respectively. Based upon her experience of the customers who

decide to buy something, $25\%$ buy Tussie$-$Mussies, $40\%$ buy wreaths, and $35\%$ buy baskets.

What is the expected revenue per purchase?

d$.$ The crafter believes that $20\%$ of all customers she talks to will end up making a purchase. What

is the crafter's income rate $($$$/$hour$)?$