Hi, I was wondering if you could answer this for me? It requires the use of R-Studio, a software for outputting numbers. For this problem, use 4901 as the initial seed and run 10,000 iterations, please!
A salesperson in a large bicycle shop is paid a bonus if he sells more than 4 bicycles a day. The probability of selling more than 4 bicycles a day is only 0.40. If the number of bicycles sold is greater than 4, the distribution of sales is as shown in the table below. The shop has four different models of bicycles. The amount of the bonus paid out varies by type. The bonus for model A is $10; 40% of the bicycles sold are of this type. Model B accounts for 35% of the sales and pays a bonus of $15. Model C has a bonus rating of $20 and makes up 20% of the sales. Finally, model D pays a bonus of $25 for each sale but accounts for only 5% of the sales. Develop a simulation model to calculate the bonus a salesperson can expect in a day. There is no bonus for selling the first 4 bicycles.
Please write the code and then give the result.
Certainly! To solve this problem using R-Studio, we can develop a simulation model that generates random numbers based on the given probabilities and calculates the bonus earned by the salesperson.
Here's the code to simulate the bonus calculation:
```R
# Set the initial seed
set.seed(4901)
# Number of iterations
iterations <- 10000
# Initialize variables
bonus <- 0
# Perform the simulation
for (i in 1:iterations) {
# Generate a random number between 0 and 1
rand_num <- runif(1)
# Check if more than 4 bicycles are sold
if (rand_num > 0.40) {
# Generate another random number between 0 and 1
model_rand <- runif(1)
# Calculate the bonus based on the model
if (model_rand <= 0.40) {
bonus <- bonus + 10 # Model A
} else if (model_rand <= 0.75) {
bonus <- bonus + 15 # Model B
} else if (model_rand <= 0.95) {
bonus <- bonus + 20 # Model C
} else {
bonus <- bonus + 25 # Model D
}
}
}
# Calculate the average bonus
average_bonus <- bonus / iterations
# Output the result
average_bonus
```
After running the simulation with the provided code and parameters (initial seed 4901 and 10,000 iterations), the result will be the average bonus earned by the salesperson in a day.
Please note that the code assumes that you have R-Studio and the necessary R packages installed on your computer.