MATH 180 Final: Math180 - Optimization
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Q: a rancher has 400ft of fencing and wants to build a corral that"s divided into 3 equal rectangles. Express the thing you want to maximize the area. Use the given into to construct an equation for perimeter as a function of variables: use the given info to relate the. 2 variables . b. save for one variable substitute into the equation to create a function with a single variable . You can"t have a negative length of fence, so x cannot be negative. If you build the corral with no width, all 400ft of fencing would = 6x. x 0 and 6x 400 x 200/3. The rst and 3rd results are obvious because they represent corrals with 0 width and length. X=100/3 maximizes the area(x=100/3 has to be a maximum because this area function forms an upside down parabola) plug our x value into the equation for y, y=100-1. 5x. y=50.
