Final answer:
The constraining resource in the Gates operation is labor capacity. Both Service A and Service B have a contribution margin per labor hour of $0, so any unused capacity can be devoted to either service.
Step-by-step explanation:
In the Gates operation, the constraining resource is labor capacity. Service A requires 3 hours of labor per unit, while Service B requires 2 hours of labor per unit. To determine which service should be provided with any unused productive capacity, we need to calculate the contribution margin per labor hour for each service. The contribution margin per labor hour for Service A is the revenue minus the variable cost divided by the labor hours per unit. For Service B, the contribution margin per labor hour is calculated the same way.
- Contribution margin per labor hour for Service A = ($0 - $0) / 3 hours = $0
- Contribution margin per labor hour for Service B = ($0 - $0) / 2 hours = $0
Since both services have a contribution margin per labor hour of $0, any unused capacity can be devoted to either service without affecting profit. There is no difference in the contribution margin per labor hour between Service A and Service B.