Firebreaks in rectangular strips

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Question

A forest in the shape of a 50 km by 50 km square has firebreaks in rectangular strips 50 km by 0.01 km. The trees between two firebreaks are called a stand of trees. All firebreaks in this forest are parallel to each other and to one edge of the forest, with the first firebreak at the edge of the forest. The firebreaks are evenly spaced throughout the forest. The total area lost in the case of a fire is the area of the stand of trees in which the fire started plus the area of all the firebreaks. Find the number of firebreaks that minimizes the total area lost to the forest in the case of a fire. If a firebreak is 50 km by b km, find the optimal number of firebreaks as a function of b. If the width, b, of a firebreak is quadrupled, how does the optimal number of firebreaks change?

Reference no: EM133853705

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