00:01
Okay, first let's find revenue.
00:02
Revenue is x times price, which is 61x minus 0 .1x to the 3 halves.
00:10
Now the profit is revenue minus cost, which is 61x minus 0 .1x to the 3 halves minus 31x minus 450.
00:25
This is minus.
00:32
Okay, now these two become 30x.
00:38
So let's take the derivative now.
00:42
30 minus 3 over 2 times 0 .1, so 0 .3 over 2 x to the 1 half.
00:54
Set it to zero.
00:55
So we have 60 over 0 .3 is equal to root x.
01:03
And from here x is, so from here x is square root of 200, which is about 14 .414.
01:13
So price will be 61 minus 0 .1 times root x, which is perfect, which is root x is square root of 2...