# Æ for the optimum value q 0 of q 7 7¹ äåæ¹³ 0

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− Æ & For the optimum value Q 0 of Q. 7 ÄÅÆ±¹³! = 0 ⇒ 5 6±²³7² » · = Æ & Æ % + Æ & 7 J J ÄÅÆ±¹³!⎥ »¶» L = ±Æ % + Æ & ³¸±¹ · ³ > 0 Hence F(Q 0 ) = Á Â Á Ã ¿Á Â gives the conditions for finding the optimum value of Q as Q 0 . Remarks: If C 3 = C 4 , the formula reduces to G 6±²³7² = À J » · , which shows that the optimum level of inventory in the beginning of the period is the median of the distribution of the demand. Example: A baking company sells cake by the pound. It makes a profit of 50 paise a pound on every pound sold on the day it is baked. It disposes of all cakes not sold on the date it is baked; at a loss of 12 paise a pound. If demand is known to be rectangular between 2,000 and 3,000 pounds, determine the optimum daily amount baked and calculate optimum level of inventory if demand is instantaneous.

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Solution: C 3 =Re.0.12 C 4 =Re.0.50 and f±D³ = 1 100 , 612 2000 ≤ ² ≤ 3000 5 1 1000 » ¼¶J·· = 1 1000 ±¹ − 2000³ 1 1000 ±¹ − 2000³ = 0.50 0.12 + 0.50 or Q · = 2000 + 50 × À··· )J = 2806 per pound. References Kanti Swarup, P.K.Gupta, Man Mohan, Operation Research, Sultan Chand & Sons publisher, New Delhi. Ravindran, Phillips & Solberg, Operations research, John Wiley, Singapore, (2007). Richard Levin & David Rubin, Quantitative approach to Management, Mc GrawHill International, (1992). Pannerselvam, R. (2006) Operation Research, Prentice Hall of India Private Limited, New Delhi, Second Edition.
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