solve

[jack_carver]

Given:
a,b,c,d and T

find (x,y) such that ax+by=T and cx+dy is maximum !

this can be easily solved using Extended Euclid algorithm.But is there any simpler way using calculus ??

Thank you

[quzah]

The math forum is that way: ----->


Quzah.

[brewbuck]

Given:
a,b,c,d and T

find (x,y) such that ax+by=T and cx+dy is maximum !

this can be easily solved using Extended Euclid algorithm.But is there any simpler way using calculus ??

Thank you

Using calculus, there are two ways to solve it:

1. Direct solution. Solve the constraint equation for y. Substitute this into the second equation to get an equation only in x. Take the derivative, set it equal to zero, solve for x. Now back-substitute the value of x into the constraint equation and solve for y.

2. Lagrange multipliers. Check Wikipedia.