Q1 (4+4+2=10 marks): The Bahria Enclave sports boosters group has scheduled a two-day fund-raiser to buy uniforms for all of the area's educational institutions and to enhance infrastructure. Donations will be sought via cellphone and face to face throughout the day and night. The boosters group has arranged for the contribution of time by local university students to collect donations. The average contribution from each kind of contact is as follows, and so is the time required for a volunteer to seek each type of donation: Night Day 8 7 Mean interview time (minutes) Via cellphone In person 20 14 19 18 Mean donation ($) Via cellphone 38 34 In person The boosters group has arranged for numerous companies and vehicle dealers to provide fuel and cars for college students to utilise in order to make a maximum of 600 in-person contacts during the fundraising campaign. Because of the privacy issues, the night contacts through cellphones should not exceed double of the day contacts through the same medium. Day contacts and night contacts by cellphones should be higher in number than three times of day contacts and five times of night contacts in person, respectively. Throughout the campaign, the college students will give a total of 24 hours during the day and 45 hours at night. The booster club president want to know how many various kinds of donor contacts to plan during the campaign in order to maximise overall contributions. 1. Formulate and show the mathematical model for this integer-programming problem. 2. Solve the model for this issue using integer-programming approach. 3. What is the difference between the integer and non-integer solutions to this issue in terms of the total maximum amount of donations?