The Rudy Snow Company makes custom snowboards. The company’s profit can be modeled with the relation , where x is the number of snowboards sold (in thousands) and y is the profit (in hundreds of thousands of dollars).
a) How many snowboards does the company need to sell to break even? (Find the zeros)
b) How many snowboards does the company need to sell to maximize their profit? (find the vertex)
To find the zeros of the relation, we need to find the value of x when y is equal to zero. Therefore, we set the equation equal to zero and solve for x:
0 = 3x - 6
3x = 6
x = 2
Therefore, the company needs to sell 2,000 snowboards to break even.
To find the vertex of the relation, we need to determine the value of x that maximizes y. The x-coordinate of the vertex can be found using the formula: x = -b / (2a). In this case, a = 3 and b = -6.
x = -(-6) / (2*3)
x = 6 / 6
x = 1
Substituting this value of x back into the equation, we can find the corresponding value of y:
y = 3(1) - 6
y = 3 - 6
y = -3
Therefore, the company needs to sell 1,000 snowboards to maximize their profit.