00:01
In the solution of this question, first of all we will let here y and z are be the length, breath and height respectively.
00:23
And now our volume will be as volume is length into breath into height, so this will be as x multiplied by y multiplied by z.
00:31
So as the subject of constraint we can see here z is j.
00:38
Is x comma y comma z is equal to 2 x z added by 2 y z added by xy added by xy which is given here 48 and now using the method of lawrence multipliers by norange multiplier we look at the values of x y z and lambda values for x y z and lambda such that v, our value for the delta v, is equal to lambda delta j.
01:27
And here, j is x, y, comma, z, which is equal to 48.
01:33
So this gave up as equation, which is v at x as lambda g x, v -it -y as lambda g -y.
01:46
V -y et z, which is lambda, j -z.
01:52
And now 2xz plus 2 -y -z plus xy plus x -y which is equal to 48.
02:00
So our solution for force part as x, sorry, y -z is equal to lambda, 2 z plus y -y.
02:10
Solution for second part will be xy is equal to lambda 2 z plus x solution for third part is xy is equal to lambda 2x plus 2y and for the fourth value we have 2x z plus 2y z plus 2y which is already we have 48 so here is the first set of solution and now further, as we know that there is no general rule for solving the system of equation of equation.
02:54
So sometimes we will use the ingenuity required.
02:58
So for the solution of fifth part, as xyz is equal to lambda to xz added by xy from by multiplying first equation by x, second equation by y and third equation by z, we will find our solutions here.
03:15
For the second equation, we will multiply that by y, so we will get here x, y, z again, lambda, 2 y z added by xy, 7th equation will be as xyz is equal to lambda, 2y z plus 2 y, 2x, sorry for this mistake, and 2y z...