For a new product that will be released nationwide, the revenue function is R⁡(x)=−0.007⁢x^2+18,125⁢x and the cost function is C⁡(x)=428,000+13,532⁢x In both functions, x is the number of units produced. How many units does the company need to sell to break even? Round your answer to the nearest thousand.

Break-even occurs when revenue equals cost: −0.007x² + 18,125x = 428,000 + 13,532x. Rearranging gives 0.007x² − 4,593x + 428,000 = 0, whose larger solution is about 656,050 units. Rounded to the nearest thousand, that is 656,000 units, choice B. The smaller solution is only about 93 units; the larger solution is the nationwide sales level asked for here.

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