Suppose that the profit, p, for selling bumper stickers is given by p(x) = 0.1x2 + 8x - 50.
What is the minimum number of bumper stickers that must be sold to make a profit?
a.
6
c.
10
b.
2
d.
15
x^2 + 80 x - 500 = 0
x = [ -80 +/- sqrt (6400 + 2000) ] /2
x = [ -80 +/- 91.7 ] / 2
use + result
x = 5.82
so 6
You set up a hot chocolate stand at a football game. The cost of your supplies is $75.You charge $0.50 for each cup of hot chocolate
Write a function that represents the profit P for selling c cups of hot chocolate.
To find the minimum number of bumper stickers that must be sold to make a profit, we need to find the x value that minimizes the profit function p(x) = 0.1x^2 + 8x - 50.
To do this, we can find the x-coordinate of the vertex of the parabola formed by the profit function. The x-coordinate of the vertex is given by the formula: x = -b/2a
In the equation p(x) = 0.1x^2 + 8x - 50, we can see that a = 0.1 and b = 8.
Substituting these values into the formula, we get:
x = -(8) / (2 * 0.1)
x = -80 / 2
x = -40
Since the number of bumper stickers must be a positive value, we can disregard the negative value of x.
Therefore, the minimum number of bumper stickers that must be sold to make a profit is 40.
None of the provided options (a, b, c, d) include the correct answer.
To find the minimum number of bumper stickers that must be sold to make a profit, we need to determine the x-value that corresponds to the minimum value of the profit function p(x) = 0.1x^2 + 8x - 50.
To do this, we can use calculus. The minimum value of a quadratic function occurs at the vertex, which can be found using the formula x = -b/2a, where a, b, and c are the coefficients of the quadratic equation in the form ax^2 + bx + c.
In this case, the coefficient of x^2 is 0.1, and the coefficient of x is 8. There is no constant term, so c = -50. Using the formula, we can find the x-value of the vertex:
x = -b/2a = -8 / (2 * 0.1) = -8 / 0.2 = -40.
Since selling a negative number of stickers does not make sense in this context, we can conclude that the minimum number of bumper stickers that must be sold to make a profit is 40.
However, none of the answer choices provided match 40. So, none of the given options (a, b, c, or d) is correct.