Question

To generate new leads for business, Gustin Investment Services offers free financial planning seminars at major hotels in Southwest Florida. Gustin conducts seminars for groups of 25 individuals. Each seminar costs Gustin $3500, and the average first-year commission for each new account opened is $5000. Gustin estimates that for each individual attending the seminar, there is a 0.01 probability that he/she will open a new account.
a. Determine the equation for computing Gustin's profit per seminar, given values of the relevant parameters.



b. What type of random variable is the number of new accounts opened?



c. Construct a spreadsheet simulation model to analyze the profitability of Gustin's seminars. Would you recommend that Gustin continue running the seminars?



d. How large of an audience does Gustin need before a seminar's expected profit is greater than zero?

Answer 1

Answer:

(A) The equation for computing Gustin's profit per seminar; given the values of the relevant parameters is:

π = 0.01AC - 3500

Where π = profit per seminar

A = attendance per seminar

C = commission earning per new account opened

(B) A continuous random variable

(C) No

(D) An audience of 71 persons

STEP BY STEP EXPLANATION:

(A) Profit is equal to total revenue minus total cost.

TR = PAC

Where P = probability that an attendee will open a new account

A = number of attendees per seminar

C = commission Gustin gets from each new account opened.

TC = $3,500

Where cost of organizing 1 seminar is constant at $3,500

So the function for profit per seminar is given thus:

π = TR - TC = 0.01AC - 3500

(B) There are 2 types of random variable; discrete random variable and continuous random variable

We say the number of new accounts opened (NNAO) is a continuous random variable because it is not specific. It is a function of both P and A. It depends on both P and A.

From the profit function or equation we have, we can see that you can't derive the exact NNAO per attendee. It is based on probability so if you were to measure it distinctly, you would have a very minimal value.

Discrete random variables occur in specific intervals e.g. 4, 5, 6,... while continuous random variables occur over an interval; e.g. 4.01, 4.02, 4.03,...

(C) Constructing a spreadsheet simulation model to analyze the profitability of Gustin's seminars, I would not recommend that Gustin continue running the seminars!

(D) The question points to A; which is the total attendance per seminar.

So if we calculate profit with the values given in the full question, we see that profit is negative, hence Gustin is running at a loss with 25 people attending one seminar.

π = (0.01 × 25 × 5000) - 3500

π = -$2,250

So, to make a profit greater than zero, we first check how many attendees it takes for TR to equal TC or for Profit to equal 0.

We set pie π to zero.

0 = (0.01 × 5000 × A) - 3500

0 = 50A - 3500

50A = 3500

A = 70 attendees

So Gustin needs an audience of more than 70 persons before a seminars expected profit will be greater than zero.