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Formulate and solve an integer programming model for this problem.
Athletic boosters club for Beaconville has planned a 2-day fund-raising drive to purchase uniforms for all local high schools and to improve facilities. Donations will be solicited during the day and night by telephone and personal contact. The boosters club has arranged for local college students to donate their time to solicit donations. The average donation from each type of contact and the time for a volunteer to solicit each type of donation are as follows:
Average Donation ($)
Average Interview Time (min)
Phone
Personal
Day
$16
$33
6
13
Night
17
37
7
19
The booster club has gotten several businesses and car dealers to donate gasoline and cars for the college students to use to make a maximum of 575 personal contacts daily during the fund-raising drive. The college student will donate a total of 22 hours throughout the day and 43 hours at night during the drive.
The president of the boosters club wants to know how many different types of donor contacts to schedule during the drive to maximize total donations. Prepare and solve an integer programming model for this problem. What is the difference in the total maximum value of donations between the integer and non-integer rounded- down solutions to this problem?
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