The variable cost (V) of manufacturing a product varies according to the equation V = 4q where q is the quantity produce...

Question

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 = 400/q. How many units should be produced to minimize the total cost (V + F)?

A. 5  B. 4  C. 7  D. 6

Accepted Answer

Among the given options, q = 5 units yields the minimum total cost of Rs.100. Variable cost V = 4q grows as production rises, while the fixed-cost component F = 400/q falls. Their sum C(q) = 4q + 400/q is a convex curve with a unique minimum. We find this minimum using calculus (or the AM-GM inequality) and then identify which given option yields the smallest cost value.