Lecture 1

# Question 3 is it useful to increase the demand of r

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Question 3: Is it useful to increase the demand of R to 73, or more? Question 4: If increasing market demand of R to 72.48 costs money, how much the company would like to pay for it? No more than 7794 – 7664 = \$130

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23 Business Meanings 2400 1064 15 10 : D Machine 2400 2285 16 6 15 : C Machine 2400 2400 16 28 12 : B Machine 2400 2400 10 10 20 : A Machine : s Constraint of Tightness 60 , 36 . 16 , 82 . 81 : Solution Optimal = + + = + + = = + + = = + + = = = Q P R Q P R Q P R Q P R Q P Question : If the company can make certain effort to increase the available time of some of the machines, which machine(s) should be given the extra available time? Used Available
24 Limitations of the Model Linear assumption Profit function may not be linear Continuous assumption Production units may have to be integers Certainty Maximum demand may be random Machine may subject to failure May be too simplified (abstraction) We may not be able to find a schedule to run the machines

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25 Strategy Guidance Product R is the most profitable product, should be produced as many as possible Product P is more profitable than Q Machines A and B are bottle neck machines
26 Summary 1. To model a problem to an LP, we need Identify decision variables Analyze relevant constraints, and use mathematics to formulate each constraint Write the objective as a function of decision variable An LP model requires all equations to be linear functions of the decision variables 2. An LP can be solved by existing software 3. Business meanings can be inferred from the solution of an LP model
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