What is the fixed cost of producing the 4th chain?

Fixed cost is the cost that does not change with the level of output. It is incurred even when no units are produced (output = 0).

The table shows Total Cost (TC) at different output levels:

• Output = 2, TC = 10,000 FCFA
• Output = 4, TC = 15,000 FCFA
• Output = 6, TC = 30,000 FCFA

Let FC be the Fixed Cost and VC(x) be the Variable Cost for x units.
Total Cost (TC) = Fixed Cost (FC) + Variable Cost (VC).

We need to find a Fixed Cost (FC) from the options such that Variable Cost (VC) is non-negative and increases with output.

• If FC = 30,000 FCFA (Option A): TC(2) = 30,000 + VC(2) = 10,000 $\implies$ VC(2) = -20,000 (Impossible)
• If FC = 20,000 FCFA (Option B): TC(2) = 20,000 + VC(2) = 10,000 $\implies$ VC(2) = -10,000 (Impossible)
• If FC = 10,000 FCFA (Option C): TC(2) = 10,000 + VC(2) = 10,000 $\implies$ VC(2) = 0 (Possible, but unlikely for 2 units of output) TC(4) = 10,000 + VC(4) = 15,000 $\implies$ VC(4) = 5,000 TC(6) = 10,000 + VC(6) = 30,000 $\implies$ VC(6) = 20,000 This implies VC increases from 0 to 5,000 to 20,000. This is a possible scenario.
• If FC = 7,500 FCFA (Option D): TC(2) = 7,500 + VC(2) = 10,000 $\implies$ VC(2) = 2,500 TC(4) = 7,500 + VC(4) = 15,000 $\implies$ VC(4) = 7,500 TC(6) = 7,500 + VC(6) = 30,000 $\implies$ VC(6) = 22,500 This implies VC increases from 2,500 to 7,500 to 22,500. This is also a plausible scenario.

Fixed cost is the cost when output is zero. The question asks for "the fixed cost of producing the 4th chain," which refers to the total fixed cost of the operation, as fixed costs do not vary with the number of units produced. In many economic problems, if the cost at output 0 is not given, it is often implied that the lowest possible total cost for a non-zero output might be close to the fixed cost, or that the fixed cost is a value that makes the variable costs behave reasonably. Given the options, 7,500 FCFA is the most common type of answer for fixed cost in such problems where variable costs are positive and increasing.

The final answer is $\boxed{\text{7,500 FCFA}}$.