00:01
Hello, here from the given information we get the revenue function r of x is equal to x into p of x, so that will be equal to 30 into x minus 0 .2x raised to 3 by 2.
00:20
We get the cost function c of x is equal to 9x plus 500.
00:27
In the a part we have to find the profit function.
00:32
So the profit function, it is equal to p of x will be equal to r of x minus c of x.
00:51
So therefore, p of x will be equal to 21x minus 0 .2x raised to 3 by 2 minus 3 by 2 minus 500.
01:06
Further in the b part, we have to find how many number of shirts were made to sold to obtain the maximum profit.
01:15
So taking p dash of x, which is 21 minus 0 .3 root x, p dash of x is 0.
01:26
Therefore, 21 minus 0 .3 root x is equal to 0, which implies x is, is, is 490 so it can be said that therefore 490 shirts have to be made and sold to obtain the maximum profit then in the c part it's been asked to calculate what price of shirt will be sold so at x is equal to 490 we'll substitute this in cost equation c of 490 9 into 490 plus 500 which is equal to 4 56 double 0 so therefore it can be said that at 4 56 double 0 price the shirts be sold...