00:01
Hello students, in this problem given p of x is equal to minus 40000x plus 240000x square plus 252000x.
00:22
Consider this as equation number one.
00:26
Here p represents the profit.
00:28
We have to find the production level, maximize profit.
00:43
First, differentiating equation one with respect to x, we get p dash of x is equal to minus 40000 plus 480000x plus 252000.
01:04
And equating p dash of x to zero, we get minus 40000 plus 480000x plus 252000 equal to zero and solving, we get x is equal to 0 .18.
01:32
Hence, the company produce 0 .18 unit in thousands.
01:52
That is 0 .18 units is equal to 180 units.
02:04
For the sub question b given y is equal to 3x power 3 plus 5x power 5.
02:13
We have to find the local maximum and local minimum.
02:32
Now differentiating y, we get y dash is equal to 9x square plus 25x power 4...