Shadow price

Q77 (BPP Kit)
A company uses linear programming to decide on the production and sales budget that will maximise total contribution and profit for a financial period. The optimal solution involves using all available direct labour hours, for which the shadow price is $4.50 per hour, and machine hours, for which the shadow price is $3 per machine hour. Direct labour is paid $8 per hour.

If the objective of the company is to maximise total contribution and profit in each period, how much should the company be willing to pay per hour to obtain additional direct labour hours of production capacity?

A .Up to but not including $4.5
B. Up to but not including $9.5
C. Up to but not including $12.5 => Correct ans
D. Up to but not including $15.5

The answer explains that:

The shadow price of a limiting resource is the amount above the normal variable cost that will be added to the objective function (total contribution) if one extra unit of the resource is made available.
This means that the company would increase contribution by paying up to $(8 + 4.50) = $12.50 per hour for additional labour time. However, it would not pay exactly $12.50, as this would leave it no better and no worse off than if it did not have the extra labour hour.

– Could you explain more why “this would leave it no better and no worse off than if it did not have the extra labour hour” or why the company would not pay exactly $12.50? Paying for direct labor hours at $12.50/hr, i think, is making some contribution still.

Many thanks.