A clothing designer determines that the number of shirts she can sell is given by the formula S = −4x2 + 88x − 160, where x is the price of the shirts in dollars. At what price will the designer sell the maximum number of shirts? a $2 b $11 c $20 d $324
A clothing designer determines that the number of shirts she can sell is given by the formula S = −4x2 + 88x − 160, where x is the price of the shirts in dollars. At what price will the designer sell the maximum number of shirts?
a
$2
b
$11
c
$20
d
$324
ANSWER:
The number of shirts sold is given by the formula S = -4x^2 + 88x - 160, where x is the price of the shirts in dollars. To find the price at which the maximum number of shirts will be sold, we need to find the vertex of the quadratic function.
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 = -4 and b = 88. Plugging these values into the formula, we get:
x = -88 / (2 * -4)
x = -88 / -8
x = 11
Therefore, the maximum number of shirts will be sold at a price of $11.
The correct answer is:
b) $11
IMPORTANT:
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At a price of 11$ per shirt, the designer can sell the maximum number of shirts.
The answer is (B) 11$
This question can be solved by using the graphical representation of the equations given.
First, we know that the general equation of a parabola is represented as
y = ax² + bx + c, which is also the general form for a quadratic equation.
(a,b,c are constants)
Number of Shirts sold (S) = -4x² + 88x - 160
Identifying general terms,
a = -4
b = 88
c = -160
x = Price of each shirt ($)
Thus, from the question, we conclude that the given formula can be represented in the form of a downward parabola (a<0).
(Refer to Diagram)
The maximum number of shirts, as required by the designer, can be found by identifying the vertex of the parabolic function.
The vertex of the parabola of the form ax² + bx + c is defined as :
x = (- b/2a)
Thus, the vertex of our parabola is at
x = -88/[2 * (-4)]
x = -88/-8
x = 11$
Thus, the designer would sell a maximum number of shirts at a price of 11$ per shirt.
Option b) 11$ is the right answer.
To understand more about downward parabolas, please refer to
brainly.com/question/25841639
(Image is not drawn to scale, it is made only for a representation of the shape of a downward parabola)
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