00:01
Hi, in this question, given that z equals x into y and subject to the constraints x plus 2y equals 12.
00:12
In part a, we have to form a lagrangian and first order conditions.
00:17
So, we can write it as l of x comma y comma lambda equals xy plus lambda into subject to the constraint x plus 2y minus 12.
00:29
On differentiating with respect to x, then we get dou l by dou x equals lambda plus y.
00:36
Dou l by dou y which is equal to 2 lambda plus x.
00:40
Dou l by dou lambda which is equal to x plus 2y minus 12.
00:47
On equating all the values with 0, then solve it, we get x comma y equals 6 comma 3.
01:01
So, that here the function z equals 6 into 3 which is equal to 18.
01:10
Hence, conclude that the maximum solution is 18 and here the value of x comma y equals 6 comma 3.
01:25
Next, instead of lagrangian method, we have to form z in terms of f of x.
01:30
So, here z equals x into y and x plus 2y equals 12.
01:36
We have to express in terms of x so that 2y equals 12 minus x.
01:41
Y equals 12 minus x divided by 2...