A manufacturer has determined that if it sets the price of paper at x dollars per ream, then its monthly profit can be represented by the equation P = (6000 - 400x)(x - 2).
Determine the y-intercept - I multiplied it out and found that the y-intercept was (0, -12,000)
Then it says: Determine the x-intercepts and explain what they mean. I have the answers and they say the x-intercepts are (2,0) and (15,0) I understand the (2,0) from the (x - 2), however, where did the (15,0) come from? This I do not understand.
Thanks for your help.
The y intercept is where x = 0
so -12,000 is correct
The x axis intercepts are when y, the profit, = 0
that is when x = 2 and z = 15 correct
the 15 is from
6000 - 400 x = 0
x = 60/4
x = 15
Thank you!!
To determine the x-intercepts of the equation P = (6000 - 400x)(x - 2) and explain their meaning, we need to find the values of x for which P equals 0.
Setting P = 0, we get:
(6000 - 400x)(x - 2) = 0
Now, we can use the zero product property, which states that if the product of two factors is zero, then at least one of the factors must be zero.
So we have two separate equations to solve for x:
6000 - 400x = 0 (equation 1)
x - 2 = 0 (equation 2)
Solving equation 1 for x:
6000 - 400x = 0
400x = 6000
x = 6000 / 400
x = 15
So, one x-intercept is at (15,0), which means that when the price of paper is set at $15 per ream, the company will have zero profit.
Solving equation 2 for x:
x - 2 = 0
x = 2
Thus, the other x-intercept is at (2,0). This means that when the price of paper is set at $2 per ream, the company will have zero profit.
The x-intercepts represent the points at which the profit (y) becomes zero. In other words, they indicate the price levels at which the company is neither making a profit nor incurring a loss. So, when the price of paper is set at $15 per ream or $2 per ream, the company will breakeven, having neither profits nor losses.