Refer to Problem 26.

The problem involves the choice of promotions for a food bank so as to maximize the number of meals provided.

a. Use equation (15.1) with the binary variables in your model to find the second best solution to the model from Problem 26 with two category coordinators.

b. Compare the solution you obtained in Problem 26 with two category coordinators, with the second best solution found in part (a).

c. Which solution would you recommend?

Problem 26

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.

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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