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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?
Up to but not including 4.5
Up to but not including 9.5
Up to but not including 12.5
Up to but not including 15.5
Why does it mention up to but not including instead of up to and including.
Also why the answer won’t be 4.5.As I explain in my free lectures, the shadow price is the most extra they will be prepared to pay.
Therefore they will be prepared to pay up to but not including $12.50 per hour. There is no point paying exactly 12.50 per hour because this would mean zero extra contribution.
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