Rosie's Palm Pirates, a manufacturer of electronic organizers, estimates that when x hundred Palm Pirates are made, the average cost per unit is given by C(x) = 0.4x^2 -3.68x+9.524, where C is in hundreds of dollars. What is the minimum cost per unit?
is the answer $ 10.60
I get C(x) = 1.06, which makes the cost $106, since C is in hundreds of dollars.
I forgot to move the decimal one more place.
To find the minimum cost per unit, you need to determine the x-value that corresponds to the minimum point on the graph of the function C(x). This can be done by finding the vertex of the quadratic equation 0.4x^2 -3.68x+9.524.
The x-coordinate of the vertex 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, a = 0.4 and b = -3.68. Plugging these values into the formula, we get:
x = -(-3.68) / (2 * 0.4)
x = 3.68 / 0.8
x = 4.6
So, the x-value of the vertex is 4.6. Now, we need to find the corresponding y-value (the minimum cost per unit) by substituting x = 4.6 into the equation C(x):
C(4.6) = 0.4(4.6)^2 -3.68(4.6) + 9.524
C(4.6) = 0.4(21.16) -16.888 + 9.524
C(4.6) = 8.464 -16.888 + 9.524
C(4.6) = 1.1
Therefore, the minimum cost per unit is $1.10 (in hundreds of dollars), not $10.60 as you mentioned.