SOLVE THE FOLLOWING QUESTION WITH AN EXCEL SPREADSHEET USING SOLVER

Problem 1. Advertising Campaign Management

You are responsible for managing a TV advertising campaign to solicit donations in two states. Past experience has shown that, in each state, the total contributions are a function of the amount of money expended for TV ads in the state. Specifically, the response functions that indicate the percentage of the population that make donations as a function of the dollars spent on TV ads have the form y=1-e-ax where x represents the advertising expenditure (in thousands of dollars), y represents the percentage of the population donating and a is a parameter that differs from state to state. Your total advertising budget is $400,000 for the two states. The following information is available:

State 1 State 2

Response function parameter a 0.006 0.004

Population 750,000 600,000

Average donation per donor $2.00 $1.50

Question 1.1

Construct a table to show the total donations raised for the 81 combinations of spending in each of the states with each state's spending ranging from $120,000 to $280,000 with an increment of $20,000. Which spending combination provides the highest total donation?

Question 1.2

Suppose you want to maximize total donations given the budget limit of $400,000 on advertising.

Write out the mathematical optimization problem formulation (showing decision variables, objective, and constraints) to answer the following two questions:

(1) How should the advertising budget be spent in each state?

(2) What is the donation that will be raised as a result? Question 1.3

Compared to a Base Case plan where the total budget is allocated based on the population (that is, let the advertising spending by state be proportional to the state population), what is the improvement in total donations achieved by the optimal solution from above?Question 1.4

Suppose that you want to maximize total donations net of the cost of advertising. With this revised objective,

1) how big an advertising budget do you need to achieve the highest maximum donations net of the cost of advertising?

2) how should the advertising funds be spent by state?

3) what amount of donations would be raised as a result?