00:01
So in this question, we're told that the profit in terms of x and y is minus x squared, minus 1 .5 y squared, plus 20x, plus 35y minus xy minus xy minus 1 ,000.
00:15
And we want to determine how many units of each product should be produced and sold monthly.
00:22
So firstly, we know that dp by d x equals zero when the profit is at a maximum.
00:29
So this is minus 2x plus.
00:31
20 minus y.
00:34
So this tells us that y is 20 minus 2x.
00:39
Now we also know that the derivative of p with respect to y is going to be equal to 0 at the maximum of profit.
00:47
So this is minus 3y plus 35 minus x.
00:53
So now we can put in the fact that y is 20 minus 2x to get 0 equals minus 60 plus 6x plus 35 minus x.
01:04
So that tells us that 5x is 60 minus 35, which is 25.
01:10
So x is 5.
01:12
Now y is 20 minus 2x, so y is 20 minus 10, which is 10.
01:18
So we have x equals 5 and y equals 10...