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    IBHardCalculus10–12

    Optimization Problem

    Problema de Otimização

    A farmer has 200200 m of fencing to enclose a rectangular field next to a river (no fence needed along the river). Find the dimensions that maximize the area.

    A band of wavy lines across the top stands for the river. Below it a shaded rectangle is the field. Its left and right sides are drawn as heavy fence lines and both are labelled x, and the bottom side is a heavy fence line labelled y. The top side, along the river, is drawn as a light dashed line and marked as needing no fence. No lengths are given.riverxxyno fence needed

    Let xx = width (two sides). Then length =200−2x= 200 - 2x. Maximize A=x(200−2x)A = x(200 - 2x).

    Solution

    Step 1 of 6

    1. 1.A(x)=x(200−2x)=200x−2x2A(x) = x(200 - 2x) = 200x - 2x^{2}