00:01
Hi, in this question, it is given that a company has a monopole pricing of the two products whose quantities are given as q1 equal to 525 minus 3 .55 p1 plus 0 .8 p2 and q2 is equal to 783 minus 4 .55 p2 plus 1 .45 p1 where p1 and p2 are the prices of the two different products.
00:33
So, the company has to maximize the sales revenue.
00:38
So, here we can write sales revenue r is equal to q1 times p1 plus q2 times p2.
00:51
So, now let us put the value of q1 and q2 here.
00:54
So, this will be p1 multiplied by 525 minus 3 .35 p1 plus 0 .8 p2 plus p2 times q2 is 783 minus 4 .55 p2 plus 1 .45 p1.
01:16
So, if we solve this, we will get r is equal to minus 3 .55 p1 square plus 525 p1 plus 2 .25 p1 p2 minus 4 .55 p2 square plus 783 p2.
01:42
Now, we will take the partial derivative of r to find the maximum revenue.
01:49
So, we can write for maximum sales revenue del r del p1 should be equal to 0.
02:01
So, from here we will get one equation and then del r over del p2 should be also equal to 0.
02:08
Now, if we differentiate this r partial with respect to p1, so the p2 will be acting as a constant.
02:15
So, this del r over del p1 will be equal to minus 7 .10 p1 plus 525 plus 2 .25 p2.
02:33
The rest of term will become 0...