Stevie Zonoi wants to optimize her business. Suppose it is possible to choose a
ID: 1169441 • Letter: S
Question
Stevie Zonoi wants to optimize her business. Suppose it is possible to choose a service rate > the arrival rate, for Zononi’s Garage in order to minimize the cost of repairing vehicles. Let’s choose an objective function where
C() = c1 L+c2()
where c1 is the waiting cost per customer per unit time and c2 is the operating cost per unit time as a function of the service rate . If we assume for simplicity that c2() = c2, then because from queueing theory, we know that
L = /() (L:= avg. number of customers waiting and in service) we obtain the total cost function:
C()= c1/() +c2
o Find an expression for the optimal service rate .
o Program an app with App Inventor so Stevie Zononi can determine how she can set the service rate for her garage. She has to estimate the workload every day so she does not work overtime. Please include appropriate screen shots of your app. design template, blocks editor, and phone simulator. *Use appinventor2*
Explanation / Answer
a.
total cost function is
C()= c1/() +c2
Minismisng the cost function, FOC is dC/d =0
dC/d =-)= -c1/() ^2+C2=0
*= +SQRT(C2/ c1)
*= -SQRT(C2/ c1) (this is not optimal solution as service rate > the arrival rate)
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