Question

How many items must be sold to obtain weekly profit of 300$

Answer 1

Profit= Revenue - Cost

`\begin{gathered} 300=106x-0.4x^2-70x-20 \\ 300=-0.4x^2+36x-20 \\ 0.4x^2-36x+20+300=0 \\ 0.4x^2-36x+320=0 \\ \end{gathered}`

Next step, solving the previous quadratic equation

`\begin{gathered} \Delta=(-36)^2-4\cdot0.4\cdot320 \\ \Delta=(-36)^2-4\cdot0.4\cdot320 \\ \Delta=784 \end{gathered}`

Finding the roots

`\begin{gathered} x_{_(1,2)}=\frac{-(-36)\pm\sqrt[]{784}}{2\cdot0.4} \\ x_{_(1,2)}=\frac{36\pm\sqrt[]{784}}{0.8} \\ x_1=\frac{36+\sqrt[]{784}}{0.8}=(36+28)/(0.8)=(64)/(0.8)=80 \\ x_2=\frac{36-\sqrt[]{784}}{0.8}=(36-28)/(0.8)=(8)/(0.8)=10 \end{gathered}`

Answer: 10 or 80 items