Given:
[tex]c=75x+2600\\[/tex]; where c is cost in dollars and x is items sold
[tex]r=225x-x^{2}[/tex]; where r is revenue in dollars and x is items sold
Equations:
[tex]x=\frac{-b\±\sqrt{b^2-4ac}}{2a}[/tex]
Answer:
For cost and revenue to be equal, the company should produce and sell 20 or 130 items.
[tex]x=20\\[/tex] or [tex]x=130[/tex]
Step-by-step explanation:
1. Set the equations equal to each other; [tex]75x+2600=225x-x^2[/tex]
2. Subtract [tex]225x-x^2[/tex] from each side; [tex]x^2-150x+2600=0\\[/tex]
3. Determine quadratic formula variables; [tex]a=1; b=-150; c=2600[/tex]
4. Substitute [tex]a[/tex], [tex]b[/tex], and [tex]c[/tex] into quadratic formula; [tex]x=\frac{-(150)\±\sqrt{(-150)^2-4*1*260}}{2*1}[/tex]
5. Solve quadratic formula; [tex]x_{1} = 130[/tex], [tex]x_{2}=20[/tex]
