00:01
As well as students, we are given a question that if a daily cost per unit of a producing a product by the ace company is given as $15 .56, sorry, 0 .5x dollars.
00:11
Okay.
00:11
And the price on competitive market is given as $100.
00:15
What is the maximum daily profit the a's company can expect? so first of all, what we are given? we are given the cost per unit.
00:24
Okay.
00:25
So we can directly say that here.
00:26
If the cost per unit is given as 15 plus 0 .5x.
00:32
So basically the total cost can be written as total cost will be here.
00:38
We can just write cx is equal to, okay? 15, sorry, total cost can be written as cx is equals to, okay? 15 plus 0 .5x and times of x.
00:53
It means cx comes out as equals to 15x plus 0 .5x plus 0 .5x.
00:58
5x square okay students now we are given that the price on competitive market is hundred dollar okay so revenue can be written as 100x okay on the x units so we can directly say that the revenue are x okay can be written as 100x these all terms are in the dollars okay now what we need to do we can just write profit function so profit can be written as px is equals to revenue function minus cost function okay so basically basically px comes out as equals to 100x minus 15x plus 0 .5 x square it means px is equals to 100 x minus 15 x it means 85 x okay minus 0 .5 x square okay students now what we can say here that we just what we need to do we just need to differentiate it okay so d p y d x comes out as equals to 85 minus 0 .5 times of 2 comes out as 1, 1 times of x comes out as directly x...
