Interval Of Interest Of The Objective Function

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Interval Of Interest Of The Objective Function

he minimum perimeter? a.) Write the objective function in terms of width, w. b.) Find the interval of interest of the objective function c.) Which dimensions create the minimum perimeter?
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First Step: Identify the Objective function, in this case it is the perimeter since there are no defining constants for it P = 2l + 2w Second: Identify the constraint, which is that area = 4, or l _ w = 4. a.) First: Solve the constraint for l to find the constraint in terms of w. l = 256 Ö w Second: Plug this into the objective function P = 2l + 2w to get P = 2(4/w) + 2w or simply as P = 8/w + 2w b.) First: Find a common denominator in the objective function with respect to w, (found above) P = 8/w + 2w _ P = [(8 + 2w_) Ö w] Second: Now solve the numerator to find the domain of the function (8 + 2w_) _ 2w_ = |-8| _ w_ = |-4| _ w = 2 - Put this as the interval function (0,2] c.) We found that squares have the minimum perimeter when it comes to rectangles, so the sides would b l=2 and w = 2.
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