Final answer:
The operating income for Pumpkin Inc. will increase by $363,440 if sales increase by 8,000 units, calculated by determining the contribution margin per unit and multiplying it by the increase in sales volume.
Step-by-step explanation:
The question asks how much the operating income for Pumpkin Inc. will change if sales increase by 8,000 units, when the unit selling price is $55 and the unit variable costs total $110,000 for current sales of 11,500 units.
To determine the change in operating income, we need to understand the concept of contribution margin, which is the selling price per unit minus the variable cost per unit. The contribution margin can help us calculate the impact on operating income when sales volume changes.
First, let's calculate the variable cost per unit using the information provided: the total variable costs are $110,000 for 11,500 units, which comes out to be $110,000 / 11,500 units = $9.57 per unit. Next, we take the selling price per unit ($55) and subtract the variable cost per unit ($9.57) to get the contribution margin per unit, which is $45.43.
Now, to find the change in operating income when sales increase by 8,000 units, we multiply the contribution margin per unit by the increase in the number of units sold: $45.43 * 8,000 units = $363,440. Therefore, the correct option answer is that the operating income will increase by $363,440 if sales increase by 8,000 units.