SOLVE THE FOLLOWING QUESTION WITH AN EXCEL SPREADSHEET USING SOLVER WITH CITY EXPENDITURES AS DECISION VARIABLES AND MAXIMIZE TOTAL DONATIONS AS THE OBJECTIVE
A well-known charity is interested in conducting a television campaign to solicit contributions. The campaign will be conducted in two metropolitan areas. Past experience indicates that, in each city, the total contributions are a function of the amount of money expended for TV advertisements. Specifically, the charity has estimated response functions that indicate the percentage of the population making a donation as a function of the dollars spent on TV advertising. The form of this function is, y = 1 – e(-α*x), where x represents the advertising expenditure (in thousands of dollars), y represents the fraction donating, and α is a parameter that differs from city to city. The charity has earmarked a fund of $400,000 for advertising between the two cities and wants to determine the best allocation of these funds.
a) Suppose the charity decides to maximize total donations, given its budget limit on advertising. How should advertising funds be spent, and what amount will be raised in donations as a result?
b) Suppose now that there is no pre-specified budget that the charity is limited by, but whatever amount they spend on advertising, they need to pay it back once the contributions are in. How should advertising funds be spent in this case?
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