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Applications of Quadratic Equations and Inequalities
A company's revenue earned from selling x items is given by the function $\displaystyle {R}{\left({x}\right)}={36}{x}$ , and their cost is given by the function $\displaystyle {C}{\left({x}\right)}={4}{x}^{{2}}$ . Use this function to answer the following questions.
Write a function, P(x), that represents the company's profit from selling x items. Remember that $\displaystyle {P}{\left({x}\right)}={R}{\left({x}\right)}-{C}{\left({x}\right)}$ $\displaystyle {P}{\left({x}\right)}=$
Rewrite the function as a Quadratic Equation by setting $\displaystyle {P}{\left({x}\right)}={0}$ :
Solve the inequality $\displaystyle {P}{\left({x}\right)}\ge{0}$ and use your results to fill in the boxes below. The company must sell at least units to break even. The company can sell at most units and still break even.