Question

hw sec. 2.1
score: 10/13 answered: 10/13
question 11
a company manufactures and sells cell phone cases. the revenue obtained by selling e cases is given by the formula
r = 8.4e - 0.04e²
solve the equation below to find the number of cell phone cases they must sell to receive $432 in revenue.
432 = 8.4e - 0.04e²
they need to sell or cases to make $432 in revenue.
question help: video ebook

Explanation:

Step1: Rearrange the equation

We have the quadratic - equation \(0.04e^{2}-8.4e + 432 = 0\). Multiply through by 100 to get rid of the decimals: \(4e^{2}-840e + 43200 = 0\). Then divide by 4: \(e^{2}-210e + 10800 = 0\).

Step2: Use the quadratic formula

The quadratic formula for \(ax^{2}+bx + c = 0\) is \(x=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}\). For \(e^{2}-210e + 10800 = 0\), where \(a = 1\), \(b=-210\), and \(c = 10800\). First, calculate the discriminant \(\Delta=b^{2}-4ac=(-210)^{2}-4\times1\times10800=44100 - 43200 = 900\).

Step3: Find the values of e

\(e=\frac{-(-210)\pm\sqrt{900}}{2\times1}=\frac{210\pm30}{2}\).

• For the plus - sign: \(e=\frac{210 + 30}{2}=\frac{240}{2}=120\).
• For the minus - sign: \(e=\frac{210 - 30}{2}=\frac{180}{2}=90\).

Answer:

90, 120