A cricket bat manufacturing firm assesses its variable cost to be 2x(x - 40) , where x is the number of bats produced, and the fixed cost incurred on - Mathematics MCQ Mathematics Mock Test - 2 2026 | ExamTest.live

mediumMCQMathematics Mock Test - 22026Mathematics

1 attempts0% success rate1 mark

A cricket bat manufacturing firm assesses its variable cost to be 2 x (x - 40), where x is the number of bats produced, and the fixed cost incurred on storage is R s .1200 . How many bats should be manufactured for the minimum total cost?

Solution & Step-by-step Explanation

Total Cost C (x) = Variable Cost + Fixed Cost $ C (x) = 2 x (x - 40) + 1200 $ C (x) = 2 x^{2} - 80 x + 1200 To find the minimum cost, we find the derivative and set it to zero: C^{'} (x) = 4 x - 80 Setting C^{'} (x) = 0 : 4 x - 80 = 0 ⟹ 4 x = 80 ⟹ x = 20 Check the second derivative: C^{''} (x) = 4 .Since C^{''} (x) > 0, x = 20 corresponds to a minimum.

Try it yourself before checking the explanation above.

A cricket bat manufacturing firm assesses its variable cost to be 2 x (x - 40), where x is the number of bats produced, and the fixed cost incurred on storage is R s .1200 . How many bats should be manufactured for the minimum total cost?

14 Bats

12 Bats

20 Bats

6 Bats

Practice with timed mock tests and track your performance across Mathematics.