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Linear programming problem:State University

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State University has planned six special catered events for the Saturday of its homecoming football game. The events include an alumni brunch, a parent's brunch, a booster club luncheon, a postgame party for season ticket holders, a lettermen's dinner, and a fund-raising dinner for major contributors. The university wants to use local catering firms as well as the university catering service to cater these events and it has asked the caterers to bid on each event. The bids ( in \$1,000s) based on menu guidelines for the events prepared by the university are shown in the following table.

Event
Caterer Alumni Parents Booster Postgame Lettermen's Contributor
Brunch Brunch Club Lunch Party Dinner Dinner

Al's \$12.6 \$10.3 \$14.0 \$19.5 \$25.0 \$30.0
Bon Apetit 14.5 13.0 16.5 17.0 22.5 32.0
Custom 13.0 14.0 17.6 21.5 23.0 35.0
Divine 11.5 12.6 13.0 18.7 26.2 33.5
Epicurean 10.8 11.9 12.9 17.5 21.9 28.5
Fouchess 13.5 13.5 15.5 22.3 24.5 36.0
University 12.5 14.3 16.0 22.0 26.7 34.0

The Bon apetit, Custom and University caterers can handle two events, whereas the other four caterers can handle only one. The university is confident all the caterers will do a high-quality job, so it wants to select the caterers for the events that will result in the lowest total cost.

Determine the optimal selection of caterers that will minimize total cost.