MATH 318: Operations Research

Spring 2023

Assignment 2

Due: Monday, February 27

Reading

Read: Hillier & Lieberman, Chapter 3,  Sections 1- 4

         Olinick, Section I: What is Linear Programming? 

Problems:

1.         Suppose you are following an optimal policy in the original interviewing problem as discussed in class. Show that the probability of having exactly l interview is .2, the probability of having exactly 2 interviews is .56, and compute the probability of having exactly 3 interviews. 

Find the expected number of interviews if you follow the optimal policy.

2.         Compute the expected number of interviews if you follow an optimal policy which permits up to 4 interviews. Use the solution of Problem 3(a) on Assignment 1.

3.         The computer program First_Simulation enables you to carry out the calculation of an average value using simulation. The program is written to find approximations to the average value of y where is given by the function described on Page 13 of Cooper, Bhat and LeBlanc. The program assumes that any number between 0 and .9 can be chosen, with equal likelihood,  as x. This program is written in JavaScript. To run the program, copy the file First_Simulation.html to your desktop and then open file with your favorite internet browser.

(a)       Find the average value if 50 different choices of x are made.

(b)       Examine how the average value changes if 1000 choices for x are made.

(c)        Compare the numbers obtained via simulation for estimating the average value with the number calculated in the solution of problem 2 of Assignment 1.

4.      A manufacturer of rattan chairs makes three kinds of chairs: straight back chairs, lounge chairs and rocking chairs. She uses three production areas of her plant for each type of chair. These are the cutting area, where the basic chair components are cut from stock, the painting area, where the components are painted or varnished and the assembly area, where the chairs are assembled. The time required for each of the operations for each of the chairs in minutes per chair are:

Production Area	Straight	Lounge	Rocker	Total Available Time per Week
Cutting	10	15	8	2600
Painting	6	10	8	2200
Assembling	15	25	20	3400

The profit per chair is $20 for straight back chairs, $35 for lounge chairs and  $26 for rocking chairs. Develop a linear programming formulation whose solution yields the optimal production plan per week.

5.       Complete the following exercises at the end of Chapter 3 in Hillier and Lieberman : 3.1-9; 3.1-12;  3.2-2;  3.3-2;  3.4-16a.

Watch the numbering scheme! Problems are keyed to sections in the text (3.2-2 means problem 2 corresponding to Sect. 3.2). An asterisk on a problem means there is a partial answer at the back of the text. Ignore the other annotations for now--they refer to the software options, which we'll consider later.