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Unformatted text preview: Section 3.2 - Linear Programming Problems Definition: A linear programming problem consists of a linear objective function to be maximized or minimized subject to certain constraints in the form of linear equalities or inequalities. Example 1: A farmer plans to plant two crops, A and B. The cost of cultivating crop A is $50/acre, whereas that of crop B is $20/acre. The farmer has a maximum of $4,000 available for land cultivation. Each acre of crop A requires 75 labor-hours, and each acre of crop B requires 150 labor-hours. The farmer has a maximum of 15,000 labor-hours available. If she expects to make a profit of $90/acre on crop A and $100/acre on crop B, how many acres of each crop should she plant in order to maximize her profit? (Set-up the linear programming problem.) Example 2: Deluxe River Cruises operates a fleet of river vessels. The fleet has two types of vessels: A type-A vessel has 60 deluxe cabins and 96 standard cabins, whereas a type-B vessel has 40 deluxe cabins and 160 standard...
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