A political party wants to campaign for the forthcoming elections. The party has planned to allocate party volunteers to the four constituencies the party plans to contest in. Each volunteer visits his/her assigned constituency, meets voters, and seeks votes for their party. Sometimes volunteers can arrange a public meeting and reach out to many voters. Each volunteer can meet around 50 voters a day. Each volunteer needs R500 per day toward his or her personal and publicity material expenses. The following table lists the minimum number of voters the party plans to reach and the available campaigning period before the Election Day.

The party wants to determine the number of volunteers required to campaign in each constituency while maximizing their reach to voters.
a. Formulate an integer programming model for this problem.
b. Solve this model by using the computer.

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Constituency 1 Constituency 2 Constituency 3 Constituency 4 Min. voters to reach 4500 9000 6500 5000 Period (days) 10 12 12 10 Budget allowed in ² 50000 90000 72000 50000