Porisma

A hint to get started

Optimise a flower-bed under a wall-building time budget

A flower-bed for a large garden consists of an xx m by yy m rectangle topped by a semicircle of diameter xx m. A low wall takes 33 hours per metre along the straight parts and 99 hours per metre around the semicircular arc. A total of 180180 hours is available.

Use differentiation to find x,yx,y giving maximum area. marks

Expand diagram

Use the scrollbars or arrow keys to inspect details.

Flower-bed made of a rectangle of width x and height y with a semicircle of diameter x on top. Only the bottom x, two sides y, and outer semicircular arc form the wall; the joining diameter is dashed and internal.
Flower-bed made of a rectangle of width x and height y with a semicircle of diameter x on top. Only the bottom x, two sides y, and outer semicircular arc form the wall; the joining diameter is dashed and internal.
Flower-bed made of a rectangle of width x and height y with a semicircle of diameter x on top. Only the bottom x, two sides y, and outer semicircular arc form the wall; the joining diameter is dashed and internal.

[2008/I/7]

CJC · Review problems · Question 10

Weight the straight and curved lengths by their different construction times.

Read the worked solution