00:01
Okay, we're given this production function.
00:04
We're told that the revenue is 8q, 8 per unit produced.
00:12
The cost is 2l plus k.
00:14
L of course is labor and k is capital.
00:21
The profit is always revenue minus cost.
00:26
We wanna maximize the profit given all this other information.
00:35
So our objective function looks like this.
00:38
We have three lagrange multipliers because we have three constraints.
00:48
Okay, then we take the derivatives.
00:54
There are eight variables.
00:57
We have eight derivatives we have to take.
01:30
Of course, the last three are derivatives with respect to lagrange multipliers.
01:36
They reproduce the constraints.
01:58
We set them all equal to zero.
02:00
So we have eight equations and eight unknowns, but they're fairly easy to solve.
02:20
Equation one tells us lambda two is minus one...