During its productive years an apple tree can produce $1.75 \times 10^{4}$ apples. How many apples can be harvested from an orchard of 600 trees?
A. $1.05 \times 10^{6}$
B. $1.05 \times 10^{5}$
C. $1.05 \times 10^{7}$
D. $10.5 \times 10^{7}$

Step 1 ：The problem is asking for the total number of apples that can be harvested from an orchard of 600 trees, given that each tree can produce \(1.75 \times 10^{4}\) apples. This is a multiplication problem. We need to multiply the number of trees by the number of apples each tree can produce.

Step 2 ：Let's denote the number of trees as \(n\) and the number of apples per tree as \(a\). So, \(n = 600\) and \(a = 1.75 \times 10^{4}\).

Step 3 ：The total number of apples, \(t\), can be calculated by multiplying \(n\) and \(a\). So, \(t = n \times a\).

Step 4 ：Substituting the values of \(n\) and \(a\) into the equation, we get \(t = 600 \times 1.75 \times 10^{4}\).

Step 5 ：Solving the equation, we find that \(t = 1.05 \times 10^{7}\).

Step 6 ：\(\boxed{1.05 \times 10^{7}}\) is the total number of apples that can be harvested from an orchard of 600 trees.