Ecology of Wheat:
- Wheat is a rabi (winter) crop that thrives in cool and dry climates.
- It requires a temperature range of 10-15°C during germination and 21-26°C during grain filling.
- The crop needs 50-100 cm of annual rainfall.
- It grows best in well-drained loamy or clayey soils with a pH between 6.0 and 7.5.
- The primary wheat-producing states in India include Uttar Pradesh, Punjab, Haryana, Madhya Pradesh, and Rajasthan.
The slope of the tangent to the curve \( x = \sin\theta \) and \( y = \cos 2\theta \) at \( \theta = \frac{\pi}{6} \) is ___________.
Solve the following L.P.P. by graphical method:
Maximize:
\[ z = 10x + 25y. \] Subject to: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]