00:01
Hello students, we are given a question here.
00:02
Short run production function is given as q is equals to 6 l squared minus 0 .4 l cube.
00:08
We need to find those questions answers.
00:11
So first is find the value of l that maximizes the average product.
00:16
So here we are given the product is, production function is q is equals to 6 l square minus 0 .4 times l cube.
00:24
Okay.
00:25
So first of all, we need to find the average products.
00:28
So basically, average.
00:31
Product will be here we can just write will be the total product q divided by l so basically 6 l square minus 0 .4 times l cubed divided by l so what we will get let's say this is a average product q is a average quantity is equals to 6 l minus 0 4 times l square okay so when we differentiate it a d of a cube divided by dl so so what we will get 6 minus 0 .4 times of 2.
01:03
It means 0 .8, okay, students, and l.
01:06
Now, we can make it equal to 0.
01:10
So basically, what we will get here, 6 minus 0 .8l is equals to 0.
01:16
It means 0 .8l is equals to 6 and l is equals to 6 divided by 0 .8.
01:22
Can be written as 60 divided by 8.
01:24
Okay, students.
01:26
Now, here we are supposed to know that when we solve it, what we will get, will be 7 .5.
01:32
Okay, this is the value of l for which average product goes maximum.
01:38
Now we will go to the second part, find the maximizes output.
01:42
So here first of all, what we are given, q is equals to 6l is square minus 0 .4 times l cube.
01:50
So when we differentiate it dq by dl, we will get 6 times to 12.
01:55
12...