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5-2 - 5-2 Linear programming Here's a typical linear...

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5-2 Linear programming Here's a typical linear programming problem: 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 unknowns Let v = # vans to hire b = # buses to hire Step 2 : write down the constraints on b and v as a system of inequalities v 0 b 0 40b + 8v 400 3b + v 36 Step 3 : write down the objective function (that which must be maximized or minimized) cost = 100v + 1200b (minimize) 5-2 p. 1

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Step 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 satisfy the constraints e.g. the point (11, 2): b=11, v=2
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