Question

8.26 At a copy center, when a typical color copier is used by customers, the center makes a profit at a rate of $1 per minute while the center loses at a rate of $0.50 per minute when the copier is idle. On average, the probability that a color copier is busy being used is 0.40. (a) Sketch a typical realization of this two-state random process. (b) Over a period of a 15-hour day, how much profit per hour is the copy center likely to make?

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Answer 1

8.26) Solution : Given that: profit rate = $ I per min loss rate profit rate eXT $0.50 pesimin porofit for time period 'T': a ) x busy probability TXJ xo.4 = 0.4T Now Consider lass function for I 0.5 XT X0.6 = 0.3 Sketch for a stale tandem Puction: Amount Profit function Loss function + Time is o Now we need to find profit per bows: In 1 min, profit is $1 . Boy bomin, profit is $60 In i min , paofit is $0.5 Por → Noco profit rate = $60 | how & loss rate = $30/ how Mesa Consider for i hover, copy centre busy for Copying Hence Go% time is free. ...profit per hown 60 x 0.4-30 X 0.6 24 - 18 or Gomin , profie is $30 is 40% of 6 Hence perefit per hour = $6 /hour