Answer:
The correct answer is $100,000.
Explanation:
Following is the information provided:
Sales @$10 per unit                                  $4,000,000
Cost of goods @$8 per unit                    ($3,200,000)
Operating cost @$0.75 per unit             <u>  ($300,000)  </u>
Profit for the year                                     <u>   $500,000  </u>
Now the company has to calculate variable costs that are relevant here. The variable cost included in cost of goods sold is:
Variable costs per unit = (Cost of goods sold - Fixed Costs included in Cost of goods) / Units Sold
The units sold can be calculated by dividing Sales with selling price per unit. Which is:
Number of units sold = $4,000,000 / $10 per unit = 400,000 Units
Now putting values in the above equation, we have:
Variable costs = ($3,200,000 - $1,200,000) / 400,000  = $5 per unit
Other variable operating costs per unit will also be calculated as it is also a variable cost here. Because the variable operating cost per unit is relevant here for decision making, it would be calculated as under:
Variable operating cost per unit = (Operating Cost - Fixed cost included) / Number of units sold
By putting values, we have:
Variable operating cost per unit = ($300,000 - $100,000) / 400,000 units 
= $0.5 per unit
Now we will calculate Net benefits arising from this order. The relevant costs are variable costs and relevant revenues are at the rate $7.5 per unit.
Cost - Benefit analysis:
Savings from sales = 50,000 units * $7.5 per unit =                     $375,000
Variable cost = 50,000 units * $5 per unit =                                 ($250,000)
Variable operating cost per unit = 50,000 units * $0.5 per unit=<u> (</u><u>$25,000)</u>
Net Saving / (Loss)                                                                           $100,000
So the net gain from this opportunity will be $100,000.