00:01
In this problem, we are provided that the cost function c of x equals to 80 times x plus 180 ,000, and the revenue function r of x equals to negative 0 .04 times x squared plus 600 times x.
00:24
And we are asked to find out the profit function p of x.
00:30
We know that the profit is the difference between the revenue and the cost.
00:37
So we have p of x equals to r of x minus c of x.
00:43
Substituting the values of the functions, we have 0 .04 times x squared plus 600 times x minus 80 times x minus 180 ,000.
00:59
So, simplifying this by combining the like terms, we have negative 0 .04 times x squared plus 520 times x minus 180 ,000.
01:14
So this is a final answer for the profit function which we denote as p of x.
01:24
Next, we are asked to find out the marginal profit function, that is mp of x.
01:35
So the marginal profit equals to the first derivative of x, sorry, the first derivative of p of x.
01:45
So let us differentiate p of x...