28. the profit function for a new product is given by $p(x) = -4x^2 + 28x - 40$, where $x$ is the number sold in thousands. how many items must be sold for the company to break even?
a) 2000 or 5000
b) 2000 or 3500
c) 5000 or 7000
d) 3500 or 7000

Question

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": false, "concepts_used": [], "new_concepts": [ "Break-Even Analysis", "Quadratic Equations" ], "current_concepts": [ "Break-Even Analysis", "Quadratic Equations" ] } ## Set profit function to zero $$ -4x^2 + 28x - 40 = 0 $$ ## Solve the quadratic equation $$ \begin{aligned} x^2 - 7x + 10 &= 0 \ (x - 2)(x - 5) &= 0 \ x = 2 \quad &\text{or} \quad x = 5 \end{aligned} $$ ## Convert units to thousands $$ \begin{aligned} 2 \times 1000 &= 2000 \ 5 \times 1000 &= 5000 \end{aligned} $$

a) 2000 or 5000

b) 2000 or 3500

c) 5000 or 7000

d) 3500 or 7000

{ "subject": "Mathematics", "question_type": "Multiple Choice", "knowledge_point": [ "Mathematics", "Algebra", "Quadratic Equations" ] }

Sovi.AI - AI Math Tutor

QUESTION IMAGE

Question

Explanation:

Set profit function to zero

Solve the quadratic equation

Convert units to thousands

Answer: