the cost, $c$, to produce $b$ baseball bats per day is modeled by the function $c(b) = 0.06b^2 - 7.2b + 390$. what number of bats should be produced to keep costs at a minimum?

$\bigcirc$ 27 bats
$\bigcirc$ 60 bats
$\bigcirc$ 174 bats
$\bigcirc$ 390 bats

Question

the cost, $c$, to produce $b$ baseball bats per day is modeled by the function $c(b) = 0.06b^2 - 7.2b + 390$. what number of bats should be produced to keep costs at a minimum?

$\bigcirc$ 27 bats
$\bigcirc$ 60 bats
$\bigcirc$ 174 bats
$\bigcirc$ 390 bats

Accepted Answer

{ "quality": "clear", "question_count": 1, "skills_matched": [ "step_cot", "multiple_choice_formatter", "explain_then_answer", "quick" ], "needs_drawing": true, "concepts_used": [ "Vertex of a Quadratic Function" ], "new_concepts": [], "current_concepts": [ "Vertex of a Quadratic Function", "Quadratic Functions" ] } ## Identify the quadratic function coefficients $$ C(b) = 0.06b^2 - 7.2b + 390 \implies a = 0.06,\ b = -7.2,\ c = 390 $$ ## Calculate the vertex coordinate for the minimum $$ b = -\frac{-7.2}{2(0.06)} = \frac{7.2}{0.12} = 60 $$

27 bats

60 bats

174 bats

390 bats

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QUESTION IMAGE

Question

Explanation:

Identify the quadratic function coefficients

Calculate the vertex coordinate for the minimum

Answer: