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Unformatted text preview: 52 Linear programming Here's a typical linear programmingproblem:A senior class of at most 400 students will rent buses and vans for a class trip. Each bus can transport 40 students plus 3 chaperones, and costs $1200 to rent. Each van can transport 8 students plus 1 chaperone, and costs $100 to rent. There are at most 36 chaperones available.How many vehicles of each type should be rented in order to minimize the cost? What is the minimum cost?Here’s how to solve it:Step 1: identify and name the unknownsLetv = # vans to hireb = # buses to hireStep 2: write down the constraintson b and v as a system of inequalitiesv ≥b ≥40b + 8v ≥4003b + v ≤36Step 3: write down the objective function (that which must be maximized or minimized)cost = 100v + 1200b(minimize)52p. 1Step 4: graph the system of inequalities from step 2:•shaded area (solution of the system of restraint inequalities)•represents all combinations of b and v•that satisfythe constraints•e.g. the point (11, 2): b=11, v=2...
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This note was uploaded on 12/11/2011 for the course MATH 1324 taught by Professor Staff during the Spring '11 term at Austin Community College.
 Spring '11
 Staff
 Linear Programming

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