the profit a company makes from producing $x$ tabletops is modeled by the equation $p(x) = 480x - 2x^2$. for what number of tabletops does the company make a profit of $\$0$?

100 tabletops
120 tabletops
240 tabletops
480 tabletops

Question

the profit a company makes from producing $x$ tabletops is modeled by the equation $p(x) = 480x - 2x^2$. for what number of tabletops does the company make a profit of $\$0$?

100 tabletops
120 tabletops
240 tabletops
480 tabletops

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [ "Zeros of Quadratic Functions", "Solving Quadratic Equations" ], "new_concepts": [], "current_concepts": [ "Zeros of Quadratic Functions", "Solving Quadratic Equations", "Quadratic Modeling Interpretation" ] } ## Set the profit equation to zero $$ P(x) = 480x - 2x^2 = 0 $$ ## Factor the quadratic equation $$ 2x(240 - x) = 0 $$ ## Solve for non-zero x $$ \begin{aligned} &x = 0 \quad \text{or} \quad 240 - x = 0 \ &x = 240 \end{aligned} $$

100 tabletops

120 tabletops

240 tabletops

480 tabletops

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Zeros of Quadratic Functions" ] }

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QUESTION IMAGE

Question

Explanation:

Set the profit equation to zero

Factor the quadratic equation

Solve for non-zero x

Answer: