The maximum area in square units of an isosceles triangle inscribed in an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ with its vertex at one end of the major axis is

A mathematical model written to construct a rectangle of maximum area out of a thread of length $10 \mathrm{cm}$ is given by,

$max\left\{tb\right\}$ such that $2\left(t+b\right)=10, l, b>0$ where $l \& b$ are the length  & breadth of the rectangle.

This is not linear programming problem because