00:01
A firm has a monthly average cost in dollars given by c equal to 41 ,000 over x plus 300 plus x, where x is the number of units produced per month.
00:12
The firm can sell its product in a competitive market for $2 ,100 per unit.
00:17
If the production is limited to 550 units per month, find the number of units that give maximum profit.
00:25
First, we need to recall how do we find the profit p of x will be equal to the difference between the revenue to the cost.
00:47
Where our revenue here, r of x, will be equal to the price of the product, 2 ,100 times the number of units sold.
01:02
The cost, c of x, is given to us in our problem statement and is equal to 41 ,000 over x plus 300 plus x.
01:18
So now, let's insert these two equations into our profit function.
01:22
We'll find that p of x is equal to 2 ,100 x minus 41 ,000 over x minus 300 minus x.
01:40
So now we have the profit function that we want to maximize...