the Ruby Snow Company makes custom snowboards. the company's profit can be modelled with the relation y=6x^2+42x-60,where x is the number snowboards sold(in thousands) and y is the profit (in hundreds of thousands of dollars)
How many snowboards does the company need to sell to maximize their profit?
The answer is 3500. But I keep getting 1350000
I wish I knew if you were using calculus or algebra or geometry....
But if you examine the profit function, it is a parabola that turns upward, and it only has a minimum vertex, no max. The second term should be -42 to make it work.
To find the number of snowboards the company needs to sell to maximize their profit, we first need to understand the concept of maximizing a quadratic function. The function given is:
y = 6x^2 + 42x - 60
In this case, x represents the number of snowboards sold (in thousands), and y represents the profit (in hundreds of thousands of dollars).
To maximize the profit, we need to find the vertex of the quadratic function. The vertex represents the highest point (maximum value) of the parabola.
The formula for the x-coordinate of the vertex of a quadratic function in the form ax^2 + bx + c is given by:
x = -b / (2a)
From the given function, we know that a = 6 and b = 42.
Substituting the values into the formula, we get:
x = -42 / (2 * 6)
x = -42 / 12
x = -3.5
Now, it is important to note that the number of snowboards sold cannot be negative, so we need to consider the absolute value of the x-coordinate. Therefore, the company needs to sell 3.5 thousand snowboards to maximize their profit.
However, since the prompt asks for the total number of snowboards (not in thousands), we need to multiply the answer by 1000:
3.5 * 1000 = 3500
Thus, the company needs to sell 3500 snowboards to maximize their profit.