A manufacturing firm sets the price per unit as p(x) = 400 - α x^2 , where α is a constant and x is the units demanded. If the marginal revenue when 1 - Mathematics MCQ Mathematics Mock Test - 1 2026 | ExamTest.live

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A manufacturing firm sets the price per unit as p (x) = 400 - α x^{2}, where α is a constant and x is the units demanded. If the marginal revenue when 10 units were in demand was zero, then the value of α is:

Solution & Step-by-step Explanation

Revenue function R (x) = x \cdot p (x) $ R (x) = x (400 - α x^{2}) = 400 x - α x^{3} M a r g ina lR e v e n u e (MR) i s t h e d er i v a t i v eo f R(x) : MR = \frac{d R}{d x} = 400 - 3 α x^{2} G i v e n t ha t MR = 0 w h e n x = 10 : 0 = 400 - 3 α (10)^{2} $ 0 = 400 - 300 α 300 α = 400 α = \frac{400}{300} = \frac{4}{3}

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A manufacturing firm sets the price per unit as p (x) = 400 - α x^{2}, where α is a constant and x is the units demanded. If the marginal revenue when 10 units were in demand was zero, then the value of α is:

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