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
There is clearly a typo in the above, since the function is a parabola which opens upward, and so has no maximum.
If we go with
y = -6x^2+42x-60
then that works out to
y = -6(x^2-7x+10)
= -6(x-5)(x-2)
The vertex is at x = 3.5, so that means 3500 boards.
You know, if you keep getting wrong answers, it would help to show your work, so it can be corrected.
To find the number of snowboards the company needs to sell to maximize their profit, we can use the vertex formula for a quadratic function. The vertex formula states that the x-coordinate of the vertex of a quadratic function in the form of y = ax^2 + bx + c is given by:
x = -b / (2a)
Given the equation of the profit function as y = 6x^2 + 42x - 60, we can identify:
a = 6
b = 42
c = -60
Using the vertex formula, we can substitute these values to find the x-coordinate of the vertex:
x = -42 / (2 * 6)
x = -42 / 12
x = -3.5
However, since the number of snowboards sold cannot be negative, we discard this solution. The company cannot sell a negative number of snowboards.
Therefore, the company needs to sell 3500 snowboards (in thousands) to maximize their profit.
To find the number of snowboards the company needs to sell in order to maximize their profit, we need to find the vertex of the quadratic equation. The vertex represents the maximum point on the graph of the equation.
The equation given is y = 6x^2 + 42x - 60, where y represents the profit and x represents the number of snowboards sold (in thousands).
To find the vertex, we can use the formula: x = -b/2a, where a, b, and c are coefficients of the quadratic equation in the form ax^2 + bx + c.
In this case, a = 6, b = 42, and c = -60.
Substituting these values into the formula x = -b/2a:
x = -42 / (2 * 6)
x = -42 / 12
x = -3.5
However, since the number of snowboards sold cannot be negative, we discard the negative value and consider its positive counterpart.
Therefore, the company needs to sell 3,500 snowboards (x = 3500) to maximize their profit.
So, the correct answer is indeed 3500, not 1350000.