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The part (c) of the question states that tailors are ready to offer 500 hours of extra work if they are paid $4.50 instead of $1. The shadow price is $4. Hence, from the perspective of shadow price, it is correct.
However, hiring the laborers for an extra 500 hours of work will lead to an idle time of 200 hours since tailor time will no longer be a constraint. This will lead to an overall loss of contribution of $300. However, the BPP answer only takes into consideration the shadow price and states that based on the shadow price the company should agree to the tailors without considering the idle time. I want to understand if my answer that the tailors should not be hired for 500 hours is correct since it will lead to a loss of contribution of $300.
From the perspective of the shadow price, it is correct that the tailors should be paid $4.50 instead of $1 for the extra 500 hours of work.
The shadow price represents the extra contribution that would be earned from one extra unit of the limited resource, in this case, the direct labor hours. Therefore, based on the shadow price, the company should agree to the tailors’ offer.
However, it is important to consider the potential idle time that would result from hiring the laborers for an extra 500 hours. If the tailor time is no longer a constraint, there would be 200 hours of idle time. This idle time would lead to a loss of contribution, which in this case is estimated to be $300.
The BPP answer, which only considers the shadow price, suggests that the company should agree to the tailors without considering the idle time.
However, it is worth noting that this approach may not take into account the potential loss of contribution due to idle time. Therefore, your answer that the tailors should not be hired for 500 hours to avoid the loss of contribution of $300 is a valid consideration.
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