M141_Notes_3-2.doc - Math 141 Lecture Notes Section 3.2...

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Math 141 Lecture Notes Section 3.2 Linear Programming Problems A linear programming problem consists of a linear objective function to be maximized or minimized subject to certain constraints in the form of linear equations or inequalities. Maximization Problems Example 1: A farmer plans to plant two crops, A and B. The cost of cultivating crop A is $40/acre, whereas that of crop B is $60/acre. The farmer has a maximum of $7400 available for land cultivation. Each acre of crop A requires 20 labor-hours, and each acre of crop B requires 25 labor-hours. The farmer has a maximum of 3300 labor-hours available. If she expects to make a profit of $150/acre on crop A and $200/acre on crop B, how many acres of each crop should she plant in order to maximize her profit?
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Minimization Problems Example 2: Super Gasoline Company operates two refineries with different production capacities. Refinery A can produce 4000 gallons per day of premium gasoline, 2000 gallons per day of super gasoline, and 1000 gallons per day of regular gasoline. On the
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