A rectangular banner has a red border and a rectangular white center. The width

Question

A rectangular banner has a red border and a rectangular white center. The width of the border at top and bottom is 9 in., and along the sides it is 6 inches. The total area of the whole banner is 23 square feet. What should be the dimensions (height and width) of the banner, if the area of the white center is to be maximal possible? A rectangularbox with a square base and a cover is to contain 1000 cm3. If the cost per square cm for the bottom is $2, for the top is $4, and for each side is $3, what should, the dimensions be in order to minimize the cost?

Explanation / Answer

(L -1) * (H - 1.5) = A      
L = length of banner
H = height of banner
A = central area of banner
A = L H - H - 1.5L + 1.5
Taking partial derivatives w.r.t L and H
L = 1.5
H = 1
This tells us that L = 1.5 H
1.5 H^2 = 23     since L * H = 23
H = 3.92
L = 5.87

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