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Production output by a manufacturing company is restricted by a shortage of supplies of Material X and skilled labour Y. Material X costs $10 per kilogram.
It has been determined using linear programming that at the profit maximizing level of output,all available quantities of Material X would be fully utilised and the shadow price(dual price) of Material X would be $6 per kilogram. Skilled labour Y has a shadow price of $0 , but existing staff would be willing to work overtime for an additional $2 per hour.
another supplier has now offered to supply additional quantities of Material X , but at the price of $14 per kilogram.
Would the company increase profit by (1) purchasing Material X at the higher price or (2) employing skilled worker Y to work overtime ?Please help me to solve this.
thanks
I assume that you have watched the free lecture on linear programming, and that therefore you know that the shadow price is the most extra that we would be prepared to pay for one extra unit of the limited resource.
Therefore for materials, it will be worth buying more (because it will increase profits) provided that the cost of extra materials is less than $16 ($10 + $6).
For labour, because the shadow price is $0, it is not worth paying any more than they are currently paying.
I think that should answer your question 🙂
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