Question

The owner of a local car dealership has just received a call from a regional distributor stating that a $5000 bonus will be awarded if the owner's dealership sells at least 10 new cars next Saturday. On an average Saturday, this dealership has 75 potential customers look at new cars, but there is no way to determine exactly how many customers will come this particular Saturday. The owner is fairly certain that the number would not be less than 40, but also thinks it would be unrealistic to expect more than 120 (which is the largest number of customers to ever show up in 1 day). The owner determined that, on average, about one out of ten customers who look at cars at the dealership actually purchase a car - or, a .10 probability (or 10% chance) exists that any given customer will buy a new car.

a. Create a spreadsheet model for the number of cars the dealership might sell next Saturday

b. What is the probability that the dealership will earn the $5000 bonus?

c. If you were this dealer, what is the maximum amount of money you would be willing to spend on sales incentives to try to earn this bonus?

Answer 1

Answer;

Given That,

The owner of a local car dealership has just received a call from a regional distributor stating that a $5000 bonus will be awarded if the owner's dealership sells at least 10 new cars next Saturday.

an average Saturday, this dealership has 75 potential customers look at new cars

fairly certain that the number = less than 40, unrealistic to expect more than 120

(a). Create a spreadsheet model for the number of cars the dealership might sell next Saturday

In order to construct a spreadsheet model used for the number of cars the dealership might sell next

Saturday follow the steps given below:

Now,

Calculate the number of customers that will arrive to look at new cars is obtained by the formula
given below:

Number of customers =ROUND(Psi Triangular ( , average people arrive on saturdays,))

To calculate number of cars sold on Saturday the function used is given below:

Number of cars sold =PsiBinomial ( Number of customers, Probability of customers buying new car)

It is known that number of sales needed for bonus is 10.
To know if bonus exists or not the function used is:

IF (Number of cars sold>=Sales Needed for bonus, 1,0) + Psi Output( )

To obtain the probability that the dealership will earn the $5000 bonus use the formula:

P(Bonus=$5000) = PsiMean (Bonus)

The maximum amount of money spends on sales incentive to try to earn the bonus is found in the formula given below

5000 x Probability that the dealership will earn the $5000 bonus

The result obtained is given below:

Number of Customers	61
Number of Cars Sold	8
Sales needed for bonus	10
Bonus? (1=yes, 0=no)	0
b	0.2784
c	$1,392

(b). What is the probability that the dealership will earn the $5000 bonus?

The probability that the dealership will earn the $5000 bonus is 0.2784

(c) If you were this dealer, what is the maximum amount of money you would be willing to spend on sales incentives to try to earn this bonus?

The maximum amount of money spends on sales incentive to try to earn the bonus is $1,392