Articulate and solve an integer programming model for this problem.
Athletic boosters club for Beaconville has deliberate a 2day fundraising drive to purchase uniforms for all the local high schools as well as to improve facilities. Donations will be petitioned during the day and night by telephone and personal contact. The boosters club has decided for local college students to donate their time to solicit donations. The average donation from each kind of contact and the time for a volunteer to solicit each kind of donation are as follows

Average Donation ($)

Average Interview Time (min)


Phone

Personal

Phone

Personal

Day

$16

$33

6

13

Night

17

37

7

19

The booster club has gotten numerous 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 fundraising drive. The college student will contribute a total of 22 hours during the day and 43 hours at night during the drive.
The president of the boosters club needs to know how many different types of donor contacts to schedule during the drive to maximize total donations. Formulate as well as solve an integer programming model for this problem. What is the dissimilarity in the total maximum value of donations among the integer and noninteger rounded down solutions to this problem?