To determine the net operating income under variable costing, we can use the following approach:

1. Calculate Total Sales: $\text{Total Sales} = \text{Selling Price per Unit} \times \text{Units Sold} = 35 \times 25,000 = 875,000$

2. Calculate Total Variable Costs:

   • Total Variable Production Cost: $\text{Variable Production Cost per Unit} \times \text{Units Sold} = 8 \times 25,000 = 200,000$
   • Total Variable Selling and Administrative Cost: $\text{Variable Selling and Administrative Cost per Unit} \times \text{Units Sold} = 5 \times 25,000 = 125,000$
   • Total Variable Costs: $200,000 + 125,000 = 325,000$

3. Calculate Contribution Margin: $\text{Contribution Margin} = \text{Total Sales} - \text{Total Variable Costs} = 875,000 - 325,000 = 550,000$

4. Subtract Fixed Costs:

   • Total Fixed Costs: $\text{Fixed Production Costs} + \text{Fixed Selling and Administrative Costs} = 82,500 + 60,000 = 142,500$
   • Net Operating Income: $\text{Net Operating Income} = \text{Contribution Margin} - \text{Total Fixed Costs} = 550,000 - 142,500 = 407,500$

Conclusion

The company's net operating income under variable costing would be: $\boxed{407,500}$

Answer:

$407,500

Would you like further details on any part of the calculation? Here are some additional questions that may extend your understanding:

1. How would net operating income change if more units were sold?
2. What would be the impact if variable costs per unit increased?
3. How would absorption costing affect net operating income?
4. How would fixed costs impact the break-even point?
5. What effect would increasing production have under variable costing?

Tip: In variable costing, fixed production costs are treated as period costs and expensed in the period they are incurred, unlike absorption costing.