Linear Prog COP4355_Part_47

# Linear Prog COP4355_Part_47 - Chapter 16 Waiting...

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192 Chapter 16 Waiting Lines (Queues) 16.6 (continued) (b) A 11 U = < 1 11 < 2N S 2N 11 < N 2 N > 5.5 N = 6 workers (c) S 1 1 1 1 1 T = = < < S - A 2N - A 4 2N - 11 4 4 < 1 4 < 2N - 11 15 < 2N 2N - 11 N > 7.5 N = 8 (d) S 1 1 T = = = 1 hr. S - A 12 - 11 (e) ( ) ( ) Q A 11 11 T = = = = 55 mins. S S - A 12 12 - 11 12 (f) S A 11 N = = = 11 customers S - A 12 - 11 (g) ( ) ( ) ( ) 2 2 Q 11 A N = = = 10.08 customers S S - A 12 12 - 11 (h) ( ) ( ) 2 2 11 11 P = 1 - = .0833 .8403 = .07 = 7% 12 12       (i) s (N 3) 0 1 2 P = 1 - (P + P + P) = 1 - (.0833 + .0764 + .07) = .7703 = 77%

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Solutions Manual and Workbook 193 16.7 A = .75 S = .5D - .05D 2 S 1 = .5 - .05 = .45 Infeasible (S < A) S 2 = 1 - .2 = .8 N Q2 = 14.0625 S 3 = 1.5 - .45 = 1.05 N Q3 = 1.7860 S 4 = 2 - .8 = 1.2 N Q4 = 1.0420 S 5 = 2.5 – 1.25 = 1.25 N Q5 = .9 Cost 2 hands (3)(2)(\$40) + \$750(14.0625) = \$10,786.875 3 hands (3)(3)(\$40) + \$750 (1.7860) = \$1,699.500 4 hands (3)(4)(\$40) + \$750 (1.0420) = \$1,261.500* 5 hands (3)(5)(\$40) + \$750 (.9) = \$1,275.000 4 dock hands is optimum 16.8 (a) A = 45/hr S = 60 = 12/hr 5 Minimum number of servers = 45 = 3.75 = 4 servers 12 (b) Traffic density = ( ) A 45 = = 0.9375 NS 4 12 (Round to .95 and use table for P 0 ) P 0 = .005 ( ) ( ) N Q 0 2 A S T = P N - 1 ! NS - A S
194 Chapter 16 Waiting Lines (Queues) 16.8 (continued) ( ) ( ) ( ) ( ) 4 2 45 12 12 .005 3 ! 4 12 - 45 = ( ) ( ) ( ) ( ) 12 197.75 = .005 6 9 = (.22hr.)(60) = 13.2 min. (c) ( ) ( ) Q Q N = AT = 45 .22 = 9.9 waiting (d) Average number per line =

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