00:02
In this question, the price of a product is given by the function p, where x is the number of units produced and sold, and the revenue is the price multiplied by the number of units sold.
00:15
And we are asked to find the price which would yield the revenue of $9 ,430.
00:22
In other words, we are asked to solve the equation, r equals to 9430.
00:27
First of all, r equals to x times p, and since p equals to 134 minus 0 .025 x, we're going to write the revenue function as a quadratic function.
00:47
134x minus 0 .025x squared.
00:53
This is a formula for the revenue function in terms of x, and we want this to be equal to 9430.
00:59
This gives us a quadratic equation for finding x.
01:05
So let's rewrite it so that it starts with x squared.
01:16
And also let's subtract 9 ,430 from both sides.
01:28
Now let's multiply both sides by negative 1.
01:33
And we are going to get 0 .025 x squared minus 134x plus 9 ,430 equals to 0.
01:46
Now we are going to use the quadratic formula to solve this equation.
01:51
We need to calculate a discriminant, which equals to the coefficient in front of, to the negative, to the coefficient in front of x squared, minus 4 multiplied by the coefficient in front of x squared, and multiplied by the three coefficient.
02:15
Now let's use a calculator to find a discriminant.
02:19
So we need to calculate negative 134 squared, minus 3 .4.
02:23
4 times 0 .025 and multiplied by 9 ,430.
02:37
And this equals to 17 ,013.
02:46
Now let's see if this number is a perfect square.
02:53
Unfortunately, it's not, so we are going to keep this number in this form for a while.
02:58
Now we will use this discriminant to calculate the roots.
03:02
By the quadratic formula, x equals to the negative coefficient in front of x.
03:07
Plus minus the square root of the discriminant and divided by 2 multiplied by the coefficient in front of x squared.
03:22
This equals to 134 plus minus the square root of 17 ,013 and divided by 0 .05...