Question

Fullerton Bakery advertises fresh baked cookies which it sells for $3.50 per lb.
The demand per day for cookies follows normal distribution with mean 8 lbs
and standard deviation 1 lb. If the cookies are not sold at the end of the day,
it sells remaining cookies to a discount store which pays either $1.00, $1.25, $1.50,
or $1.75 per lb with equal probabilities based on their requirements.
Cookies cost bakery any where from $2.00 to $3.00 per lb uniformly distributed.
Bakery has asked you to help them in calculating profit per day if they produce
9 lbs of cookies every day. Answer following questions with 1000 days simulation. What is the average of discount price bakery will get?   (Note: You can use probabilities to calculate average discount price or run 1000 simulation trials of discount prices to calculate average.) Select one: a. $1.375 b. $1.525 c. $1.235 d. Average can not be calculated If Fullerton Bakery makes 9 lbs of cookies every day, what percent of days will have a loss? Select one: a. almost 0% b. less than 10% c. more than 20% d. can not be determined If Fullerton Bakery makes 9 lbs of cookies every day, what is the average daily profit? (choose the closest answer) Select one: a. $5.21 b. $6.70 c. $7.01 d. $7.12 How many lbs of cookies per day should be produced to get highest per day profit? Select one: a. 7 lbs b. 8 lbs c. 9 lbs d. 10 lbs If Fullerton Bakery makes 10 lbs of cookies every day, what percent of days will have a loss? Select one: a. almost 0% b. less than 10% c. more than 20% d. can not be determined

Answer 1

The average of discount price bakery will get is (A) $1.375

If Fullerton Bakery makes 9 lbs of cookies every day, percent of days it will have a loss is (A) almost 0%

If Fullerton Bakery makes 9 lbs of cookies every day, the average daily profit is (B) $6.70

(A) 7 lbs of cookies per day should be produced to get highest per day profit

If Fullerton Bakery makes 10 lbs of cookies every day, the percent of days will have a loss (B). less than 10%

The complete R code for simulation is given below.

set.seed(46464)
N <- 1000
prod <- 9
demand <- rnorm(N, mean =8, sd =1)
cost <- runif(N, min=2,max=3)
dis_price <- sample(c( 1.00,1.25,1.50,1.75),N,replace=TRUE, prob=rep(1/4,4))
Discount <- (prod-demand)*dis_price
Profit <- 3.5*demand+(prod-demand)*dis_price - prod*cost
mean(Discount)
mean(Profit)
num_loss <- length(Profit[Profit<0])
num_loss/N