17-14, Joe loves to eat out in area restaurants. His favorite foods are Mexican,

Question

17-14, Joe loves to eat out in area restaurants. His favorite foods are Mexican, Italian, Chinese. and Thai. On the average, Joe pays $10.00 for a Mexican meal, $15.00 for an Italian meal. $9.00 for a Chinese meal, and $11.00 for a Thai meal. Joe's eating habits are predictable: There is a 70% chance that today's meal is a repeat of yesterday's and equal probabilities of switching to one of the remaining three. (a) How much does Joe pay on the average for his daily dinner? (b) How often does Joe eat Mexican food? . An Anahation

Explanation / Answer

---- R-code as below with RESULTS ----

## There is some data that is missing: numbe of states and transition matrix, as said above also.. taking the above transition matrix assumption, showing methodology to solve this question:-
install.packages("markovchain")
library("markovchain")

# As assumed, number of states = 3
States = c("m","i","c","t")
byRow = TRUE
sMatrix = matrix(data = c(0.7,0.1,0.1,0.1,0.1,0.7,0.1,0.1,0.1,0.1,0.7,0.1,0.1,0.1,0.1,0.7), byrow = byRow, nrow = length(States), dimnames = list(States, States))

mcr = new("markovchain", states = States, byrow = byRow,
transitionMatrix = sMatrix, name = "rest.")

## Part a
steadyStates(mcr)

# m i c t
# 0.25 0.25 0.25 0.25

## avg_cost = 0.25*(10+15+9+11) = 11.25 [Answer a.]

## --- PART 2 ---

#### Given steady state results, as above,
## On average, Joe will have Mexican food 1/4-th times (25% of the times) [Answer b.]

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