Question

21. The James Charities annual fund-raising drive is scheduled to take place next week. Donations are collected during the day and night, by telephone, and through personal contact. The average donation resulting from each type of contact is as follows:

	Phone	Personal
Day	$2	$4
Night	$3	$7

The charity group has donated enough gasoline and cars to make at most 300 personal contacts during one day and night combined. The volunteer minutes required to conduct each type of interview are as follows:

	Phone (min)	Personal (min)
Day	6	15
Night	5	12

The charity has 20 volunteer hours available each day and 40 volunteer hours available each night. The chairperson of the fund-raising wants to know how many different types of contacts to schedule in a 24-hour period (i.e. 1 day and 1 night) to maximize total donations.

Formulate the linear programming model for this problem first and then solve it using Excel.

Answer 1

21.

Let, xij = number of j type of contacts assigned to period i in one day where j = {Phone=1,Personal=2} and i ={Day=1,Night=2}

objective is to maximize donation = max 2x11+4x12+3x21+7x22

subject to,

x12+x22 <= 300 (Max personal contacts)
6x11+15x12 <= 60*20 (Max volunteer hours per day)
6x11+15x12 <= 1200

5x21+12x22 <= 60*40 (Max volunteer hours per night)
5x21+12x22 <= 2400

xij >= 0

Solving in solver we get,

Optimal category of contracts:

Phone contacts in Day = 200
Personal contacts in Day = 0
Phone contacts in Night = 480
Personal contacts in Night = 0

Maximized donation : $1840

Solver screenshot

Solver formula

Solver window