19. The central Florida high school basketball tournament pits teams from four different counties against one another. The average distance (in miles) between tournament locations in each country is given in the following table.
Problem Data
|
Orange
|
Seminole
|
Osceola
|
Volusia
|
Orange
|
0
|
30
|
45
|
60
|
Seminole
|
30
|
0
|
50
|
20
|
Osceola
|
45
|
50
|
0
|
75
|
Volusia
|
60
|
20
|
75
|
0
|
Games are officiated by certified refereeing crews from each county. Orange, Seminole, Osceola, and Volusia counties have 40, 22, 20, and 26 certified crews, respectively. During the tournament, officiating crews cannot work games in their home counties and are paid $0.23 per mile in travel costs (in addition to a $50 per game officiating fee). (Assume each officiating crew travels to games in a single vehicle.)
Additionally, crews from one county cannot work more than 50% of the games in any other single county. It is anticipated that Orange, Seminole, Osceola, and Volusia counties will host 28, 24, 16, and 20 games, respectively.
a. Create a spreadsheet model to determine the least costly plan for allocating officiating crews from the various counties.
b. What is the optimal solution and associated travel cost for the referees?
c. Suppose it is desired to spend no more than $700 on referee travel expenses for these games? Is that possible? If not, determine the solution that minimizes the maximum percentage deviation from the 50% officiating requirement for each county while requiring no more than $700 in travel costs.