To solve the problem, we'll use the concept of inverse variation. The cost \( C \) of producing pairs of gloves varies inversely with the number of pairs produced \( p \). This can be expressed mathematically as:
\[ C \times p = k \]
where \( k \) is a constant.
From the information given, we know that when 5000 pairs are produced, the cost is 50 cents per pair. Therefore:
\[ C = 0.50 \quad \text{and} \quad p = 5000 \]
We can now substitute these values into the equation to find \( k \):
\[ 0.50 \times 5000 = k \]
Calculating \( k \):
\[ k = 2500 \]
Now we have established that:
\[ C \times p = 2500 \]
Next, we need to find the cost \( C \) when producing 10000 pairs (\( p = 10000 \)). We can rearrange the equation:
\[ C = \frac{k}{p} \]
Substituting \( k = 2500 \) and \( p = 10000 \):
\[ C = \frac{2500}{10000} \]
Calculating \( C \):
\[ C = 0.25 \]
Thus, the cost of producing 10000 pairs of gloves will be 25 cents per pair.