00:01
We have a cost function, c equals 40x plus 300, a revenue function, r equals 80x minus 0 .5x squared, and we want to give an expression for profit p.
00:12
The profit is simply the equal to the revenue minus the cost.
00:17
And x simply just means the number of items produced or sold.
00:22
So to give an expression for the profit, profit is the revenue minus cost.
00:27
So we take our revenue function, which is 80x minus 0 .5x squared.
00:36
And we subtract our cost function, which is 40x plus 300.
00:43
So to simplify this, we have to be careful when we're subtracting a polynomial.
00:48
So we can drop the parentheses here and just get profit equals 80x minus 0 .5x squared.
00:55
And then we're subtracting 40x plus 300, so we're just going to distribute a negative 1 there.
01:03
So minus 40x minus 300.
01:06
And then if we get this in standard form, the profit is equal to, we'll list this quadratic term first.
01:14
Negative 0 .5x squared.
01:17
We're done with that.
01:18
Then we have 80x minus 40x that are like terms.
01:21
80 minus 40 is 40, so plus 40x minus 300.
01:27
So there's the profit function.
01:31
Negative 0 .5x square plus 40x minus 300...