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Assignment#2 ADM2302X Summer 2010 Assignment # 2 LP Formulations and Applications Due Date: Monday, May 31, 2010 (Clearly state: "Submitted to...

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Assignment#2 ADM2302X Summer 2010 Assignment # 2 LP Formulations and Applications Due Date: Monday, May 31, 2010 (Clearly state: “Submitted to Prof. Phansalker” on your Assignment) At the Information Desk before 12:00 noon. ADM2302 students are reminded that submitted assignments must be neat, readable, and well-organized. Assignment marks will be adjusted for sloppiness, poor grammar and spelling, as well as for technical errors. While working together is encouraged, plagiarism on assignments will not be accepted. Each student must provide an individual original submission of completed assignments. Solutions to all exercises in this assignment are to include “managerial statements” that communicate the results of the analyses. Problem 1 The United 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 dollar value of donations resulting from each type of contact is as follows. Phone ($) Personal ($) Day Night 2 3 3 7 The charity group has enough donated gasoline and cars to make at most 300 personal contacts during one day and night. The volunteer minutes required to conduct each type of interview are as follows. Phone (min) Personal (min) Day Night 6 5 12 10 The charity has 20 volunteer hours available each day and 40 volunteer hours available each night. The chairperson of the fund-raising drive wants to know how many different types of contacts to schedule in a 24-hour period (i.e., one day and one night) to maximize total donations. a. Formulate algebraically the Linear Programming (LP) model for this problem. Dr. Suren Phansalker Telfer School of Management University of Ottawa 1
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Assignment#2 ADM2302X Summer 2010 b. Formulate this same linear programming problem on a spreadsheet and SOLVE using Excel solver (Provide a printout of the corresponding “Excel Spreadsheet” and the “Answer Report”). Problem 2 The Mill Mountain Coffee Shop blends coffee on the premises for its customers. It sells three basic blends in 1-pound bags, Special, Mountain Dark, and Mill Regular. It uses four different types of coffee to produce the blends – Brazilian, mocha, Columbian, and mild. The shop used the following blend recipe requirements. Blend Mix Requirements Selling Price/pound ($) Special Dark Regular At least 40% Columbian, at least 30% mocha At least 60% Brazilian, no more than 20% mild No more than 30% mild, at least 50% Brazilian 6.50 5.25 4.50 The cost of Brazilian coffee is $2.00 per pound, the cost of mocha is $2.75 per pound, the cost of Columbian is $2.90 per pound, and the cost of mild is $1.70 per pound. The shop has 110 pounds of Brazilian coffee, 70 pounds of mocha, 80 pounds of Columbian, and 150 pounds of mild coffee available per week. The shop wants to know the amount of each blend it should prepare each week to maximize profit. a. Formulate algebraically the Linear Programming (LP) model for this problem. b. Formulate this same linear programming problem on a spreadsheet and SOLVE using Excel solver (Provide a printout of the corresponding “Excel Spreadsheet” and the “Answer Report”). Problem #3 A classic linear programming problem involves minimizing trim loss. Here is one version of the problem: A mill cuts 20-foot pieces of wood into several different lengths: 8-foot, 10-foot and 12- foot. The mill has a certain amount of 20-foot stock on hand and orders for the various sizes. The objective is to fill the orders with as little waste as possible. For example, if two 8-foot lengths are cut from a 20-foot piece, there will be a loss of 4 feet, the leftover amount. Currently, the mill has 350 20-foot pieces of wood on hand and the following orders, which must be filled from stock on hand: Size in feet Number Ordered 8 276 10 100 12 250 Dr. Suren Phansalker Telfer School of Management University of Ottawa 2
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