Define (Any Two):
(a) Farm Management
(b) Weed
(c) Acre-inch
(a) Farm Management:
Farm management involves organizing, planning, and overseeing farm operations to maximize both productivity and profitability. It includes making decisions on resource allocation, selecting crops, managing labor, and financial planning to ensure efficient agricultural outcomes.
(b) Weed:
A weed is any undesirable plant that grows in agricultural fields, competing with crops for essential resources like water, sunlight, space, and nutrients. Weeds can greatly reduce crop yield, degrade quality, and raise production costs. Effective weed control is critical for sustainable farming practices.
(c) Acre-inch:
An acre-inch is a unit of volume used in irrigation, indicating the amount of water required to cover one acre of land with a depth of one inch.
This is roughly equivalent to 27,154 gallons (123,344 liters).
It is commonly used in irrigation planning to optimize water usage in agricultural operations.
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: \[ 0 \leq x \leq 3, \quad 0 \leq y \leq 3, \quad x + y \leq 5. \]