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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 $4.50
B. Up to but not including $9.50
C. Up to but not including $12.50
D. Up to but not including $15.50
How to solve this question?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. In this case, the shadow price for direct labor hours is $4.50 per hour.
Since the objective of the company is to maximise total contribution and profit, the company should be willing to pay up to but not including $4.50 per hour to obtain additional direct labor hours of production capacity.Therefore, the correct answer is A. Up to but not including $4.50.
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