3.3 Using shadow prices
§ The relevant cost of a resource = the normal cost + the shadow price.
§ Thus shadow prices can be used for decision making in the same way as any other relevant costs.
Illustration 8 – Using shadow prices中华考试网
Continuing the Hebrus example:
ConstraintNormal costShadow priceRelevant cost
Cutting time$10/hour$6.67/hour$16.67/hour
Assembly time$15/hour$2.50/hour$17.50/hour
Thus the most Hebrus would pay for additional cutting time (e.g. through overtime or the use of temporary staff) would be $16.67 per hour. Similarly assembly time is worth $17.50 to the firm.
These figures can also be used to assess the impact of Hebrus losing hours for any reason, such as sickness.
Test your understanding 7
Suppose a linear programming problem gives the following results.
ConstraintNormal costShadow price
Skilled labour$20/hour$12/hour
Unskilled labour$10/hourZero
Materials$5/kg$3/kg
(a) Which two constraint give rise to the optimal solution?
(b) Overtime is paid at ‘time-and -a-half’. Is it worth paying overtime to help relax constraints?
(c) A new product has been proposed with the following proposed costs and revenues
$
Selling price80
Skilled labour – 2 hours@$20/hour(40)www.Examw.com
Unskilled labour – 1 hour@$10/hour(10)
Materials – 3kg@$5/kg(15)
Profit per unit15
Assuming that the constraints cannot be relaxed, should the new product be manufactured?
发表于 2012-2-23 17:09:42
