Final answer:
To break even on the licensing rights for a new variety of rose, the greenhouse owner must produce and sell 750 rosebushes at $17 each, having a variable cost of $9 per rosebush.
Step-by-step explanation:
The owner of a greenhouse and nursery is trying to decide if it would be profitable to acquire licensing rights for growing a new variety of rosebush that they can sell at $17 each. To find out how many rosebushes need to be sold to cover the costs, one must calculate the break-even point.
The fixed costs for the licensing rights are $6,000, and the variable costs per unit amount to $9. The contribution margin per rosebush, which is the selling price minus variable cost, is $8 ($17 - $9).
To calculate the number of rosebushes needed to break even, one must divide the total fixed costs by the contribution margin per unit. This calculation reveals:
Break-even quantity = Fixed Costs / (Selling price - Variable cost per unit)
= $6,000 / ($17 - $9)
= $6,000 / $8
= 750 rosebushes
Therefore, the owner must produce and sell 750 rosebushes to break even. Any sales beyond this number would result in a profit.