A rectangular box has a square base

MATHEMATICS · Single correct · CBSE · Mathematics · Applications of Derivatives · Applications of Derivatives

Problem

A rectangular box has a square base. The sides and base cost

\$10

per square metre to manufacture, while the lid costs

\$20

per square metre. The box must have a volume of

1000\,\mathrm{m}^3

. If

x

is the length of a side of the square base and

h

is the height, what is the ratio

\frac{h}{x}

that minimizes the total manufacturing cost? (a)

1

(b)

2

(c)

1.5

(d)

3