TUTORIAL 2 Linear Programming - Minimisation Special cases Simplex maximisation 1. Innis Investments manages funds for a number of companies and wealthy clients. The investment strategy is tailored to each client’s needs. For a new client‚ Innis has been authorised to invest up to $1.2 million in two investment funds: a stock fund and a money market fund. Each unit of the stock fund costs $50 and provides an annual rate of return of 10%; each unit of the money market fund costs
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| Basic math symbols Symbol | Symbol Name | Meaning / definition | Example | = | equals sign | equality | 5 = 2+3 | ≠ | not equal sign | inequality | 5 ≠ 4 | > | strict inequality | greater than | 5 > 4 | < | strict inequality | less than | 4 < 5 | ≥ | inequality | greater than or equal to | 5 ≥ 4 | ≤ | inequality | less than or equal to | 4 ≤ 5 | ( ) | parentheses | calculate expression inside first | 2 × (3+5) = 16 | [ ] | brackets | calculate expression inside first
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REVISED M09_REND6289_10_IM_C09.QXD 5/12/08 12:01 PM Page 115 9 C H A P T E R Linear Programming: The Simplex Method TEACHING SUGGESTIONS Teaching Suggestion 9.1: Meaning of Slack Variables. Slack variables have an important physical interpretation and represent a valuable commodity‚ such as unused labor‚ machine time‚ money‚ space‚ and so forth. Teaching Suggestion 9.2: Initial Solutions to LP Problems. Explain that all initial solutions begin with X1 ϭ 0‚ X2 ϭ 0 (that
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GMAT Test 2 – Copyright 2005 by Hp Group (www.hp-vietnam.com). All right reserved. GMAT TEST 2 – MATH SECTION (37 questions‚ 75 minutes) 1. X is an even number and Y is a positive odd number. Which of the following expressions cannot be even? (a) (b) (c) (d) (e) (XY) Y X3Y3 X3 XY Y2 2. How much interest will $2‚400 earn at an annual rate of 8% in one year if the interest is compounded every 4 months? (a) (b) (c) (d) (e) $141 $150 $197 $234 $312 3. What is the value of P? (1) P is even. (2) P
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programming model given below: Decision variables x1 Units of product 1 to produce. x2 – Units of product 2 to produce. Objective function Maximize 4.0x1 + 3.6x2 Constraints Constraint 1: 11x1 + 5x2 > 55 Constraint 2: 3x1 + 4x2 < 36 Constraint 3: 4x1 – 9x2 < 0 Nonnegativity: x1‚ x2 >= 0 Solve this linear programming model by using the graphical approach (Graph paper is provided on the next page). For your graphical solution‚ Label the axes. Draw and label each constraint. Show your procedure of drawing
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While the great philosophical distinction between mind and body in western thought can be traced to the Greeks‚ it is to the seminal work of René Descartes (1596-1650)‚ French mathematician‚ philosopher‚ and physiologist‚ that we owe the first systematic account of the mind/body relationship (Wozniak). As a key figure in the Scientific Revolution‚ Rene Descartes was one of the most intelligent men in his era. With his numerous writings and works‚ he allowed us to understand modern philosophy‚ the
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Number Systems Base 2: The Binary Number System Base 8: The Octal Number System Base 16: The Hexadecimal Number System Learning Objectives • At the end of the lesson the student should be able to: – Identify the different number base system – Convert base ten numbers to base two‚ eight or sixteen – Convert base two‚ eight or sixteen numbers to base ten – Perform basic operations on various base numbers Number Base • What is a number base? A number base is a specific collection
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P118 81E Common Instructions to Candidates: 1) This is a question cum answer paper booklet. 2) Space is provided to write answers below each question. Answer should be written within the space provided. 3) This question paper has 58 questions including the matching type question. 4) Candidate should not write the answer with pencil. Answer written with pencil will not be evaluated (Except graphs‚ diagrams & maps). 5) In case of multiple choice‚ fill in the blanks and matching questions‚ scratching
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Chapter 6 Resource Masters Consumable Workbooks Many of the worksheets contained in the Chapter Resource Masters booklets are available as consumable workbooks. Study Guide and Intervention Workbook Skills Practice Workbook Practice Workbook 0-07-828029-X 0-07-828023-0 0-07-828024-9 ANSWERS FOR WORKBOOKS The answers for Chapter 6 of these workbooks can be found in the back of this Chapter Resource Masters booklet. Glencoe/McGraw-Hill Copyright © by The McGraw-Hill Companies‚ Inc. All
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| | (0‚ ∞)Question 8 Find the largest open interval(s) where the function is Increasing y = x4 - 18x2 + 81Answer | | (-∞‚ 0) | | | (-3‚ 0) | | | (-3‚ 3) | | | (3‚ ∞) | Question 9 S(x) = -x3 + 6x2 + 288x + 4000‚ 4 ≤ x ≤ 20 is an approximation to the number of salmon swimming upstream to spawn‚ where x represents the water temperature in degrees Celsius. Find the temperature that produces the maximum number of salmon.Answer | | 8°C | | | 20°C | | | 4°C | | | 12°C |
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