Question

you are designing a rectangular poster to contain 24 square inches of print. the margins at the top and the bottom are to be 1.5 inches, and the margins on the left and right are to be 1 inch. What overall dimensions will minimize the amount of paper used?

Answer 1

\[L*W = 24 \rightarrow L = \frac{24}{W}\]
\[A = (L+3)(W+2)\]
\[ A = (\frac{24}{W}+3)(W+2)\]
\[A = 30+3W+\frac{48}{W}\]
\[\frac{dA}{dW} = 3-\frac{48}{W^{2}} = 0\]
\[\rightarrow 3W^{2} = 48\]
\[W = 4 \rightarrow L = 6\]
\[A_{\min} = (6+3)(4+2) = 54\]