Chapter 5 Section 2

Chapter 5 Section 2 - 5.2 Linear Programming in two...

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5.2 Linear Programming in two dimensions: a geometric approach In this section, we will explore applications which utilize the graph of a system of linear inequalities.
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A familiar example We have seen this problem before. An extra condition will be added to make the example more interesting. Suppose a manufacturer makes two types of skis: a trick ski and a slalom ski. Suppose each trick ski requires 8 hours of design work and 4 hours of finishing. Each slalom ski 8 hours of design and 12 hours of finishing. Furthermore, the total number of hours allocated for design work is 160 and the total available hours for finishing work is 180 hours. Finally, the number of trick skis produced must be less than or equal to 15. How many trick skis and how many slalom skis can be made under these conditions? Now, here is the twist: Suppose the profit on each trick ski is $5 and the profit for each slalom ski is $10. How many each of each type of ski should the manufacturer produce to earn the greatest profit?
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Linear Programming problem This is an example of a linear programming problem. Every linear programming problem has two components: 1. A linear objective function is to be maximized or minimized. In our case the objective function is Profit = 5x + 10y ( 5 dollars profit for each trick ski manufactured and $10 for every slalom ski produced). 2.
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Chapter 5 Section 2 - 5.2 Linear Programming in two...

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