All analysis should be done in a separate Excel file.
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-EXP(-ox), where EXP means the exponential function, represents the advertising expenditure (in thousands of dollars), y represents the percentage donating, and a 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. City1 City 2 Response parameter (a) Population Average donation per donor 0.006 750,000 $2.00 0.004 600,000 $1.50 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? (10) b). Based on the answer in a), is the budget of $400,000 binding? How much more donation can be generated by a dollar increase in the budget? Please use sensitivity analysis to find out the marginal value of budget dollars (not to manually compare the solutions with different budgets). (3') c). Suppose the charity wants to maximize total donations minus the cost of advertising, given its budget limit on advertising. This would make sense if surplus advertising funds can be put toward the charity's other services.) Based on this objective, is the budget of $400,000 binding? If so, how much additional budget would the charity like to obtain? If not, how much of the budget should actually be spent? (5) 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-EXP(-ox), where EXP means the exponential function, represents the advertising expenditure (in thousands of dollars), y represents the percentage donating, and a 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. City1 City 2 Response parameter (a) Population Average donation per donor 0.006 750,000 $2.00 0.004 600,000 $1.50 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? (10) b). Based on the answer in a), is the budget of $400,000 binding? How much more donation can be generated by a dollar increase in the budget? Please use sensitivity analysis to find out the marginal value of budget dollars (not to manually compare the solutions with different budgets). (3') c). Suppose the charity wants to maximize total donations minus the cost of advertising, given its budget limit on advertising. This would make sense if surplus advertising funds can be put toward the charity's other services.) Based on this objective, is the budget of $400,000 binding? If so, how much additional budget would the charity like to obtain? If not, how much of the budget should actually be spent
