### Linear Programming

goals
Find the solution of $\displaystyle 2\left ( x-3y+1 \right )\frac{dy}{dx}= 4x-2y+1.$
Solve the following Linear Programming Problems graphically :
Minimize $Z = 3x + 5y$
subject to
$x + y \leq 4, x \geq 0$ and $y \ge 0$
Solve the differential equation: $\displaystyle \frac{dy}{dx}-y\tan x= -2\sin x$
Solve the differential equation: $\displaystyle \frac{dy}{dx}-y\tan x= -2\sin x$
If a young man rides his motorcycle at $25\ km/hr$, he had to spend $Rs.2$ per km on petrol. If he rides at a faster speed of $40\ km/hr$, the petrol cost increases at $Rs.5$ per km. He has $Rs.100$ to spend on petrol and wishes to find what is the maximum distance he can travel within one hour. Express this as LPP and solve it graphically.