CUNY Borough of Manhattan Community College Linear Programming Questions

Table of Contents
Chapter 1 (Introduction)
Special Products Break-Even Analysis (Section 1.2)
1.2 – 1.6
The Relationship Between Analytics & Management Science (Sec.
1.3)
1.7 – 1.9
1.1
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What is Management Science?
This is a discipline that attempts to aid managerial
decision making by applying a scientific approach to
managerial problems that involve quantitative factors.
Discipline not too different from medical field
Scientific approach from World War II times
1.2
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McGraw-Hill Education.
What is Management Science?
Discovery of the simplex method for solving linear
programming problems in 1947 by George Dantzig.
Limited computational power (all done by hand)
Operations research came from the idea of scientists from
WWII doing research on how to manage military
operations.
Professional society-Institute for Operations Research
and Management Sciencws
1.3
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McGraw-Hill Education.
Steps
Step 1: Define the problem and gather data (problems of too much or
too little). Advances in data quality
Step 2: Formulate a model (typically a mathematical model)
Step 3: Develop a computer based procedure for deriving solutions
to the problem from the model
Step 4: Test the model and refine it as needed
Step 5: Apply the model to analyze the problem and develop
recommendations for management.
Step 6: Help to implement teams’ recommendations
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McGraw-Hill Education.
1.4
Special Products Break-Even
Analysis
• The Special Products Company produces expensive and
unusual gifts.
• The latest new-product proposal is an iWatch with wireless
internet.
• Data:
• If they go ahead with this product, a fixed cost of $10 million is
incurred.
• The variable cost is $1000 per iWatch produced.
• The cost of each additional unit is $1000 (marginal cost) so each
iWatch sold would generate $2000 in revenue.
• A sales forecast will be obtained.
Question: Should they produce the iWatch, and if so, how
many?
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consent of McGraw-Hill Education.
1.5
Expressing the Problem
Mathematically
• Decision variable:
• Q = Number of iWatches to produce
• Costs:
• Fixed Cost = $10 million (if Q > 0)
• Variable Cost = $1000 Q
• Total Cost =
• 0, if Q = 0
• $10 million + $1000 Q, if Q > 0
• Profit:
• Profit = Total revenue – Total cost
• Profit = 0, if Q = 0
• Profit = $2000Q – ($10 million + $1000Q) = –$10 million + $1000Q,
if Q > 0
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consent of McGraw-Hill Education.
1.6
Analysis of the Problem
1.7
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consent of McGraw-Hill Education.
Objective function
• A mathematical expression that gives the measure of
performance for the problem in terms of the decision variables.
• Break even point = (Fixed cost)/(Unit revenue – Marginal cost)
= (10 mill)/(2000-1000) = 10,000
If s