Math2730: Operations Research I Page 1 Assignment 4 Due: Jun 4th, Before the review class 1. Consider the project outlined in the table below. (2 point) Activity Immediate Predecessor Present Duration Accelerated Duration Present Cost Accelerated Cost A -10 9 11 15 B -15 13 20 25 C A 10 6 9 20 D A 20 18 25 30 E C 15 10 20 35 F B 17 15 20 30 G B 12 10 15 25 H D, F 9 8 12 18 I G, H 7 6 10 15 a. Construct an activity network diagram b. Disregarding the acceleration information, how long is the project expected to take to complete? c. If the project duration was to be reduced by at least one unit of time what activity (or activities) would you crash? d. Detail the steps you would take to crash the project to its minimum duration at the lowest cost 2. A mobile phone company company services six geographical areas. The satellite distances in thousands of miles are given in the figure below. The company needs to determine the best quality message routes that should be established between each two areas in the network. Explain whether the company is facing shortest path problem or not. (2 point)
Math2730: Operations Research I Page 2 3. School of Mathematical and Physical Sciences has three professors who each teach four courses per year. Each year, four sections of Algebra, OR, and Modelling must be offered. At least one section of each class must be offered during each semester (Semester 1 and 2). Each professor’s time preference and preference for teaching various courses are given in the following table. The total satisfaction a professor earns teaching a class is the sum of the semester satisfaction. Thus, professor 1 derives a sati fiction of 3 + 6 =9 from teaching algebra during semester 1. Formulate an MCNFP that can be used to assign professors to courses so as to maximize the total satisfaction f the three professors. (2 point) 4. During the next two months, Machineco must meet (on time) the demands for three types of products shown in the Table 1. Two machines…