Profit= Revenue - Cost
[tex]\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}[/tex]
Next step, solving the previous quadratic equation
[tex]\begin{gathered} \Delta=(-36)^2-4\cdot0.4\cdot320 \\ \Delta=(-36)^2-4\cdot0.4\cdot320 \\ \Delta=784 \end{gathered}[/tex]
Finding the roots
[tex]\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}=\frac{36+28}{0.8}=\frac{64}{0.8}=80 \\ x_2=\frac{36-\sqrt[]{784}}{0.8}=\frac{36-28}{0.8}=\frac{8}{0.8}=10 \end{gathered}[/tex]
Answer: 10 or 80 items
