Question

type the correct answer in the box. use numerals instead of words. if necessary, use / for the fraction bar.
a company manufactures replacement parts for construction cranes. the fixed manufacturing cost is $2,400, and the variable cost per part is $5.50. each part is sold at $8.50.
the minimum number of parts the company must sell to break even is
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Explanation:

Step1: Define break - even formula

The break - even point occurs when total revenue equals total cost. Let \(x\) be the number of parts. The total cost \(C\) is the sum of fixed cost and variable cost. The fixed cost is \(\$2400\), and the variable cost per part is \(\$5.50\), so \(C = 2400+5.5x\). The total revenue \(R\) from selling \(x\) parts at \(\$8.50\) per part is \(R = 8.5x\). At break - even, \(R = C\), so we set up the equation \(8.5x=2400 + 5.5x\).

Step2: Solve the equation for \(x\)

Subtract \(5.5x\) from both sides of the equation: \(8.5x-5.5x=2400+5.5x - 5.5x\). This simplifies to \(3x = 2400\). Then divide both sides by 3: \(x=\frac{2400}{3}=800\).

Answer:

800