The Harvest Moon Food Bank is planning its promotional events for the next year. Harvest would like to maximize the number of meals it is able to provide based on these promotions. To do this, the food bank must effectively utilize the resources it has on-hand for holding promotional events. The table below shows the relevant resources required per event for the three categories of events (Church Food Drive, 5K Run, and Concert).

Below is the number of meals provided per event for each category and the lower and upper limit on events in the category if that category is chosen.

Each category utilized requires a category coordinator to manage the events of that category. Harvest Moon only has two category coordinators, so this limits the number of categories chosen to exactly two. Therefore, Harvest wishes to select two of the three categories and decide how many events to hold in each of the chosen categories to maximize the number of meals it can provide during the coming year.

a. Develop a mixed-integer linear model to tell which two categories to use and the number of events in that category to hold so as to maximize the meals provided over the year.

b. Create a spreadsheet model of your model developed in part (a) and solve it using Excel Solver.

c. Which categories are selected and how many events of each category will be held?

d. What is the solution if we add a third category manager and all other available resources stay the same? How many more meals are provided by adding a third-category coordinator?

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Paid Staff (hours) Volunteer Staff (hours) Supplies ($) Resources Required per Event per Category Church Food Drive 5K Run Concert Available (per year) 110 145 138 2,000 83 56 227 1,800 500 1,500 800 100,000