Interior and exterior walls of a rectangular 80,000 square foot building cost 90$ per running foot. The building is to be divided into 10 rooms by four interior walls in the x direction and one interior wall in the y direction. What should be the building dimensions if the wall cost is to be minimum.
Let be the width (in feet) and be the length. Then we have
Now,counting interior and exterior walls,there are 12 walls in the and 6 in the .the number of linear feet of the wall is
We need to minimize the cost of the walls,which means minimizing the number of linear feet of the walls
First, let's express the number of linear feet of walls as a function of single variable as follows;
Secondly, let's find where the derivative of the function is equal to zero
The total number of linear feet,and therefore the total cost of the walls, is minimum when then width is
feet and the length is feet
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