A toy manufacturing firm has its variable cost C(x) = α^2 x (β√(x) + αβ) , where x is the number of toys produced. The cost of storage and other fixed - Mathematics MCQ Mathematics Mock Test - 1 2026 | ExamTest.live

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A toy manufacturing firm has its variable cost C (x) = α^{2} x (β x + α β), where x is the number of toys produced. The cost of storage and other fixed expenses are R s . 4500 . If the marginal cost is 40 when 144 toys have been produced and α β = 1, find the possible values of α .

Solution & Step-by-step Explanation

Total Cost TC (x) = Variable Cost + Fixed Cost $ TC (x) = α^{2} x (β x + α β) + 4500 $ TC (x) = α^{2} β x^{3/2} + α^{3} β x + 4500 Marginal Cost (MC) is \frac{d ( TC )}{d x} : MC = \frac{3}{2} α^{2} β x^{1/2} + α^{3} β Substitute α β = 1 (or β = 1/ α): MC = \frac{3}{2} α^{2} (1/ α) x + α^{2} (α β) MC = \frac{3}{2} α x + α^{2} Given MC = 40 when x = 144 : 40 = \frac{3}{2} α 144 + α^{2} 40 = \frac{3}{2} α (12) + α^{2} 40 = 18 α + α^{2} α^{2} + 18 α - 40 = 0 (α + 20) (α - 2) = 0 α = 2 or α = - 20 .

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A toy manufacturing firm has its variable cost C (x) = α^{2} x (β x + α β), where x is the number of toys produced. The cost of storage and other fixed expenses are R s . 4500 . If the marginal cost is 40 when 144 toys have been produced and α β = 1, find the possible values of α .

2

- 20

20

Both (A) and (B)

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