a. Formulate an NLP model for this problem.

b. Implement your model in a spreadsheet and solve it.

c. How much money should Roger spend in each state?

d. How many campaign stops should the candidate make in each state?

e. What is the expected number of electoral votes generated by this solution?

“So it’s come down to this,” thought Roger Mellichamp as he looked around at the empty Styrofoam coffee cups and papers littering his office. When he accepted the job of campaign manager for his long-time friend’s run for the White House, he knew there would be long hours, lots of traveling, and constant media pressure. But the thing he most wanted to avoid was a close race with a final showdown just before the election. Roger knew that making decisions under those circumstances would be agonizing because the success of the campaign and, in many ways, the future of the country would hinge on those very decisions. Unfortunately, that’s just where things stand.

With only two weeks before the U.S. presidential election, Roger’s friend and the incumbent president are running neck-and-neck in the polls. So, Roger’s plans for the final two weeks of the campaign will be critical, and he wants to make sure he uses the candidate’s time and the campaign’s remaining money in the most effective way. Although the outcome of the election has been pretty much decided in most states, the electoral votes from the states of Florida, Georgia, California, Texas, Illinois, New York, Virginia, and Michigan are still up for grabs by either candidate. Roger knows they must win as many of these states as possible if his friend is to become the next president.

Several weeks ago, it became evident that the race was going to be close. So, Roger hired a statistical consultant to estimate the percentage of votes the campaign will receive in each of the states based on the amount of money the campaign spends and the number of times the candidate visits each state during the final two weeks before the election. The results of the consultant’s analysis provided the following function:

Percentage of votes state k = 1 - EXP(-aVk - bDk)

Where:

Vk = the number of times the candidate visits state k in the last two weeks of the campaign, and

Dk = the dollars (in $1,000,000s) the campaign spends on advertising in state k in the last two weeks of the campaign

The following table summarizes the consultant’s estimates of the parameters a and b for each state, along with the number of electoral votes at stake in each state:

Roger believes the candidate can make 21 campaign stops in the next two weeks, and there is $15 million left in the campaign budget available for advertising. He wants to spend at least $500,000 in each of these states in the next two weeks. He also wants the candidate to make at least one, but no more than five, campaign stops in each of these states. Within these constraints, Roger wants to allocate these resources to maximize the number of electoral votes his candidate can receive. Assume a candidate needs 51% of the vote to win in eachstate.

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Electoral Votes State Florida Georgia Texas Illinois 0.31 0.117 0.27 California 0.123 0.21 0.125 0.28 0.128 0.26 New York 0.121 0.22 0.134 0.24 0.121 0.38 0.145 13 Virginia Michigarn 13 18