To determine To calculate: Optimum time interval between successive batches of trainees, that is, m and the optimum number of trainees in a batch, that is N . Explanation Given: The mathematical model for determining the total cost per month of a training program is provided by Z ( m ) = C 1 m + D t C 2 + D C 3 ( m − 1 2 ) Here, D is demand for trainees per month; C 1 is a fixed cost of training a batch of trainees; C 2 is the variable cost of training per trainee per month; C 3 is salary paid monthly to a trainee who has not yet been given a job after training; m time interval in months between successive batches of trainees; t is the length of the training program in months; Z ( m ) is the total monthly cost of the program. The provided values for this question are D = 3 , t = 12 , C 1 = $ 15 , 000 , C 2 = $ 100 , C 3 = $ 900 . Calculation: The derivative of Z ( m ) is given by Z ' ( m ) = − C 1 m 2 + D C 3 2 Solve the equation Z ' ( m ) = 0 Thus, − C 1 m 2 + D C 3 2 = 0 D C 3 2 = C 1 m 2 Substitute the provided values of C 1 , C 3 and m in the above equation, D C 3 2 = C 1 m 2 3 × 900 2 = 15 , 000 m 2 m 2 = 10 , 000 900 m 2 = 11.11 This implies m = − 3.33 and m = 3.33 . Disregard the value m = − 3.33 as m represents months and months cannot be negative. Therefore, the time interval in months between successive batches of trainees is 3.33 months. Now, since m is not an integer. So, the two integers closest to m will be 3 and 4 . That is, m − = 3 and m + = 4

12th Edition

ISBN: 9780135240687

Author: Lial

Publisher: PEARSON

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Chapter 12, Problem 6CE

To determine

To calculate: Optimum time interval between successive batches of trainees, that is, m and the optimum number of trainees in a batch, that is N.

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Chapter 12, Problem 5CE

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