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General Aptitude
Quantitative Aptitude
GATE 2011
Medium

The variable cost (V) of manufacturing a product varies according to the equation V = 4q, where q is the quantity produced. The fixed cost (F) of production of the same product reduces with q according to the equation F = 100/q. How many units should be produced to minimize the total cost (V+F)?

  • 5
  • B4
  • C7
  • D6

Explanation

Total cost C = 4q + 100/q. Setting dC/dq = 4 - 100/q^2 = 0 gives q^2 = 25, so q = 5. The second derivative 200/q^3 > 0 confirms this is a minimum.

Source: GATE ME 2011 (2011)

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