Question

Applied Calc - A hardware store owner chooses to enclose an 800 square foot rectangular area in front of her store so that one of the sides of the store will be used as one of the four sides of the fence. If the two sides that come out from the store front cost $3 per running foot for materials and the side parallel to the store front costs $5 per running foot for materials, then find the dimensions of the fence that will minimize the cost to construct the fence. Round all dimensions to the nearest foot.

Answer 1

\[xy=800\]
\[y=\frac{800}{x}\]
\[C=3x+3x+5y\]
\[C(x)=6x+5\times \frac{800}{x}=6x+\frac{4000}{x}\]

Answer 2

take the derivative, set it equal to zero, find the critical points and check that you have a minimum