a market researcher predicted that the profit function for the first year of a new business would be p(x)= -0.3x^2 + 3x -15, where x is based on the number of items produced. will it be possible for the business to break even in its first year?
thanks
to break even, p(x) = 0
-.3x^2 + 3x - 15 = 0
times -10
3x^2 - 30x + 150=0
x^2 - 10x + 50 = 0
x = (10 ± √-100)/2
this has no real solution, the company will never make a profit.
Where did the "times -10" come from?
in order to break even he would have to produce
-o.3x^2+3x-15 factor use quadratic formula
you get two answers
5+the square root of 27
5-the square root of 27
because the second answer gives you a negative (you cant produce a negative amount of product) use the first one
10.19615242 is equivalent to x
so unless you can produce and sell .19615242 of a product which i don't know depending on the industry you just might be able, he cant break even.
To determine if the business will break even in its first year, we need to find the value of x where the profit function is equal to zero, since breaking even means that the profit is neither positive nor negative.
The given profit function is p(x) = -0.3x^2 + 3x - 15.
To find the break-even point, we set p(x) equal to zero:
0 = -0.3x^2 + 3x - 15
Now, let's solve this quadratic equation to find the value(s) of x that satisfy this equation.
We can either factor the quadratic equation, or use the quadratic formula.
Let's use the quadratic formula, which states that for an equation of the form ax^2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = -0.3, b = 3, and c = -15:
x = (-3 ± √(3^2 - 4(-0.3)(-15))) / (2(-0.3))
Simplifying further:
x = (-3 ± √(9 - 18)) / (-0.6)
x = (-3 ± √(-9)) / (-0.6)
The expression inside the square root is negative, indicating that there are no real solutions for x. Therefore, the business will not break even in its first year.
Hence, based on the given profit function, it is not possible for the business to break even in its first year.