00:03
And this particular problem, x represents the number of units produced.
00:09
So we're told right now that their revenue is $179 .95 per unit.
00:22
Now, if they increase that price by $10 per unit, this is their new revenue function.
00:31
The demand function right now, they're selling 175 ,000, units per week, but if they increase the price, they would decrease the number of items sold.
00:46
And then the cost function, we're told, is $54 per unit plus overhead costs of $225 ,000.
01:01
So these are our three functions.
01:05
Now you're asked to find the marginal revenue function, which would be drdx, so taking the derivative of this, our marginal revenue function is 10.
01:22
The marginal demand function is negative 5 ,000, and the marginal cost is 54.
01:40
Oh, and it does ask for profit.
01:42
So in order to find the profit, you need to remember that profit is your income or your revenue times your demand, because this would be how much money you're bringing in, minus your cost.
02:04
So my profit function looks kind of messy at first.
02:20
It's actually kind of hard for me to fit it all in here, isn't it? and this is actually going to be a parabola, because when you multiply this out, you'll end up with x times x, which would be x squared.
02:38
And then multiplying it all out, it comes out to be negative 50 ,000 x squared, plus 849 ,196x, plus 31 ,26 ,000, plus 31 ,26 .2 ,000...