00:01
We need to determine the profit function from the given revenue function and cost function.
00:07
And then find the break -even point.
00:10
So our profit function is equal to the revenue function minus the cost function.
00:18
So we have revenue, which is x times 210 minus 0 .25x minus in parentheses our cost function, which is 78x plus 7 .8x plus 6 .5 .5x minus in parentheses our cost function, 6 ,399.
00:35
So we're going to distribute x times 210 is 210x minus 0 times 0 .25 x squared.
00:45
We distribute our negative 1 minus 78x minus 6 ,399.
00:51
So we write it in descending exponent order.
00:56
So we have negative 0 .25x squared.
00:59
We combine like terms, so 210 minus 78, becomes plus 132x minus 6 ,399.
01:10
That is our profit function.
01:13
So now to find our break -even point, we're gonna set the costs and the revenue function equal to each other, so we're gonna have r of x equal to c of x.
01:23
So we have x times 210 minus 0 .25x equal to 78x plus 6 ,399.
01:36
So we get 210x minus 0 .25x squared.
01:41
It's equal to 78x plus 6 ,399...