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Module B: Linear Programming Linear Programming (LP) • A mathematical technique designed to help operations managers plan and make decisions necessary to allocate resources • Minimizing (cost) or maximizing (profit) Elements of LP Problems • Objective Function – what you want to maximize or minimize • Profit or cost • Constraints – things that restrict your ability to meet your objective • Production capacity, labour time, amount of materials, money • Alternative course of action • Must be several ways to allocate resources, etc • Can be expressed as a mathematical problem Example LP Problem - Glickman • Glickman Electronics • Two products to manufacture: x-pod and BlueBerry X-pod BlueBerry Available Electronics 4 hours 3 hours 240 hours Assembly 2 hours 1 hour 100 hours Profit/unit $7 $5 • How many units of each should be produced for the highest profit? Example LP model - Glickman • First, declare variables • Let x1 = Number of x-pods to be produced • Let x2 = Number of BlueBerrys to be produced • Second, present objective function • Maximize Profit = $7x1 + $5x2 I personally would use “x” and “y” instead… Cost per unit * number of units • Third, model the constraints • 4x1 + 3x2 <= 240 • 2x1 + 1x2 <= 100 • x1, x2 >= 0 Time to produce one unit * number of units cant be greater than time available Cant produce a negative number of units LP Issues • Graphing LP Problems with more than two/three variables • Nope • Just use excel to solve • Do all problems have solutions? • (ie no feasible region?) • No • May have to revisit constraints (ie add more resources, capacity, etc)