Operations Research : Applications and Algorithms
Operations Research : Applications and Algorithms
4th Edition
ISBN: 9780534380588
Author: Wayne L. Winston
Publisher: Brooks Cole
Expert Solution & Answer
Book Icon
Chapter 2, Problem 3RP

Explanation of Solution

Relating two vectors:

Suppose that Ut be the number of untenured State University faculty at the beginning of the year t, and Tt be the tenured number.

Since 75% of the untenured faculty remains untenured at the beginning of the year t+1.

Thus, the number of untenured faculty in the beginning of the year t+1 is given below:

Ut+1=0.75Ut

Also, 20% of all untenured faculties become tenured and 90% of the tenured faculty remains tenured at the beginning of the year t+1.

Therefore, the number of tenured faculties in the beginning of the year t+1 is as follows:

Tt+1=0.2Ut+0

Blurred answer
Students have asked these similar questions
At the beginning of the first day (day 1) after grape harvesting is completed, a grape grower has 8000 kg of grapes in storage. On day n, for n = 1, 2, . . . ,the grape grower sells 250n/(n + 1) kg of the grapes at the local market at the priceof $2.50 per kg. He leaves the rest of the grapes in storage where each day they dryout a little so that their weight decreases by 3%. Let wn be the weight (in kg) ofthe stored grapes at the beginning of day n for n ≥ 1 (before he takes any to themarket).(a) Find the value of wn for n = 2.(b) Find a recursive definition for wn. (You may find it helpful to draw a timeline.)(c) Let rn be the total revenue (in dollars) earned from the stored grapes from thebeginning of day 1 up to the beginning of day n for n ≥ 1. Find a recursiveformula for rn.(d) Write a MATLAB program to compute wn and rn for n = 1, 2, . . . , num wherenum is entered by the user, and display the values in three columns: n, wn, rnwith appropriate headings.Run the program for num =…
A ski rental agency has n pairs of skis, where the height of the the ith pair of skis is si . There are n skiers who wish to rent skis, where the height of the ith skier is hi. Ideally, each skier should obtain a pair of skis whose height matches her/his own height as closely as possible. We would like to assign skis to skiers so that the sum of the absolute differences of the heights of each skier and her/his skis is minimized. Design a greedy algorithm for the problem. Prove the correctness of your algorithm. (Hint: Start with two skis and two skiers. How would you match them? Continue to three skis and three skiers, and identify a strategy.)
Consider the following R code. >x = matrix(rnorm(n=500), ncol= 5) >var x = var(x). starting with var x, use 2 application s of the sweep() function, one dividing each row of the matrix and the other dividing each column, of a covariance matrix to obtain R, the correlation matrix.
Knowledge Booster
Background pattern image
Similar questions
Recommended textbooks for you
Text book image
Operations Research : Applications and Algorithms
Computer Science
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Brooks Cole