Linear Programming
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(Created page with "In my experience, Linear Programming (taught in most Algebra/precalculus and some Geometry courses) is poorly understood by teachers who have "mastered" it (ie. they know the ...") |
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I was taking an excellent course on methods for teaching mathematics at Tufts, and the professor showed this method. Nobody really got it. So the next day I brought in a model that made it clear, and everybody understood it immediately. | I was taking an excellent course on methods for teaching mathematics at Tufts, and the professor showed this method. Nobody really got it. So the next day I brought in a model that made it clear, and everybody understood it immediately. | ||
− | My idea was simply to show this as a three dimensional graph. I made it out of acetate sheets with chopsticks as axes. I used the x/y plane as the base, and graphed the feasible region on it. The z axis represents the evaluative function, so that instead of having aX + bY = c, we are using aX + bY = z. I built walls of acetate for the feasible region to show that it forms a prism in 3 space, and marked the z axis value on them as horizontal bands. The evaluative function represents a plane in 3 space that cuts across the prism. I made a piece that capped the prism where the plane would be, and drew the z axis value isoclines on it. The result looked a lot like this diagram of a prism cut by an oblique plane: | + | My idea was simply to show this as a three dimensional graph. I made it out of acetate sheets and scotch tape with chopsticks as axes. I used the x/y plane as the base, and graphed the feasible region on it. The z axis represents the evaluative function, so that instead of having aX + bY = c, we are using aX + bY = z. I built walls of acetate for the feasible region to show that it forms a prism in 3 space, and marked the z axis value on them as horizontal bands. The evaluative function represents a plane in 3 space that cuts across the prism. I made a piece that capped the prism where the plane would be, and drew the z axis value isoclines on it. The result looked a lot like this diagram of a prism cut by an oblique plane: |