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GRE
GRE Quantitative Reasoning Section

Cost Reduction and Production Capacity

Very Hard Algebra Expressions, Equations, And Inequalities

Sara is analyzing the efficiency of a manufacturing process and discovers that the cost of producing $x$ units is given by the quadratic function $$C(x) = 2x^2 - 5x + 12$$, where $C(x)$ is the total cost in dollars of producing $x$ units of materials.

She finds that reducing the cost by $50 can effectively reduce the production capacity. To identify the number of units $x$ that results in this reduced cost, Sara sets up the equation:

$$C(x) - 50 = 0$$

What is the maximum number of units $x$ that can be produced at this reduced cost?

Hint

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