chapter14a - Assignment 12 Linear Programming Model Answers...

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Assignment 12: Linear Programming: Model Answers 1. A firework company specialises in Roman candles and Catherine Wheels. A Roman candle requires 300 gms of gunpowder and 200 gms of magnesium, and 1 hollow cardboard tube. A Catherine Wheel requires 150 gms of gunpowder, 50 gms of magnesium, and a hollow paper tube. The company currently has 400 kg of gunpowder, 150 kg of magnesium, a thousand hollow cardboard tubes and a thousand hollow paper tubes. It makes $5 profit on a Roman candle and $2 profit on a Catherine wheel. Using the graphical method of linear programming, find the most profitable combination of products for the company. Let x 1 be the number of Roman candles produced, in thousands, and x 2 the number of Catherine wheels. Then we can write the following constraints: 3x 1 + 1.5 x 2 < 4 (Gunpowder) 2x 1 + 0.5 x 2 < 1.5 (Magnesium) x 1 < 1 (Cardboard Tubes) x 2 < 1 (Paper Tubes) And the total profit is given by the objective function: Z = 5x 1 + 2 x 2 simplex.eps Sketching a graph of the lines bounding these inequalities, we see that the `legal region' is bounded by the lines corresponding to the `magnesium' and `paper tubes' constraints. Sliding the `Objective Function' line across the legal region, we see it attains its greatest value at the corner point x 1 = 0.5, x 2 =1, corresponding to the production of 500 Roman Candles and 1,000 Catherine Wheels for a total profit of
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This note was uploaded on 04/16/2009 for the course ENSC 201 taught by Professor Dr.johnjones during the Fall '08 term at Simon Fraser.

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chapter14a - Assignment 12 Linear Programming Model Answers...

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