s02rec12

# s02rec12 - semester Year Cum Demand Utility of taking 0 1...

This preview shows pages 1–2. Sign up to view the full content.

Recitation 12 15.053 Introduction to Optimization May 10, 2002 1. Suppose that there are two piles of matches on a table. One pile has 5 matches and the other pile has 10 matches. The person who picks up the last match wins. At each alternating turn, my opponent or I can pick up 1 or 2 matches, but from one pile only. Assuming that I go first, how can I be sure of winning the game? Let g(j,k) = 1 if there is a forced win in the case that one pile has j matches and the other pile has k matches and it is your turn. a. Give the boundary conditions. b. Give a recursion for g(j,k). c. What is g(j,k) for all 1 j 4 and all 1 k 4? 2. A student needs to take 7 incredibly difficult subjects over the next 6 semesters. She has committed to completing at least two of these subjects by the end of Spring 2003, and completing at least four of these subjects by Spring 2004. In addition, she will not take more than two incredibly difficult subjects in any

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: semester. Year Cum. Demand Utility of taking 0, 1, or 2 incredibly difficult subjects in that term 0 1 2 Fall 2002 0 10 7 4 Spring 2003 2 10 8 6 Fall 2003 2 10 8 6 Spring 2004 4 10 8 6 Fall 2004 4 10 7 4 Spring 2005 7 10 5 1 Let f(j, term) be the maximum utility solution starting with j difficult courses taken at the beginning of term j. Thus f(7, Spring 2005) = 10 f(6, Spring 2005) = 5 f(5, Spring 2004) = 1 Compute f(j, Fall 2004) for j = 4, 5, 6, 7. Compute f(4, Spring 2003). Please show your work. Show how to computer f(2, Fall 2002) in terms of values calculated for f(j, Spring 2003). 3. Widgetco produces widgets at plant 1 and plant 2. It costs 20 x 1/2 to produce x units at plant 1 and it costs 40 x 1/3 to produce x units at plant 2. Each plant can produce up to 70 units. Each unit produced can be sold for \$10. At most 120 widgets can be sold. Formulate as an NLP the problem of maximizing profit....
View Full Document

## This note was uploaded on 12/20/2011 for the course BUS 15.053 taught by Professor Prof.jamesorlin during the Spring '05 term at MIT.

### Page1 / 2

s02rec12 - semester Year Cum Demand Utility of taking 0 1...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online