Question

# PLEASE SHOW ALL WORK IN EXCEL!!!!!!! SHOW CALCULATIONS / FORMULAS IN EXCEL!!!!!!!! Voters arrive at a...

PLEASE SHOW ALL WORK IN EXCEL!!!!!!!

SHOW CALCULATIONS / FORMULAS IN EXCEL!!!!!!!!

Voters arrive at a polling station at an average of 4 per minute (Poisson) where the service rate is 50 per hour (Poisson).

a. What is the average number of voters in the system with 5 voter booths? (10 pts)

b. What is the minimum number of voting booths needed to keep the average time in the system under three minutes? (10 pts)

PLEASE SHOW ALL WORK IN EXCEL!!!!!!!

SHOW CALCULATIONS / FORMULAS IN EXCEL!!!!!!!!

The Excel model is following:

FORMULAS:

 Cell Formula Copy to B12 =(\$B\$4/\$B\$5)^A12/FACT(A12) B12:B17 C16 =SUM(B\$11:\$B15) C16:C17 D16 =+B16/(1-\$B\$4/(A16*\$B\$5)) D16:D17 E16 =1/(C16+D16) E16:E17 F16 =\$B\$4/(\$B\$5*A16) F16:F17 G16 =+E16*B16*F16/(1-F16)^2 G16:G17 H16 =G16+\$B\$4/\$B\$5 H16:H17 I16 =G16/\$B\$4 I16:I17 J16 =I16+1/\$B\$5 J16:J17

Arrival rate = 4 per minute = 4*60 per hour = 240 per hour

a) Average number of voters in the system with 5 voter booths (L) = 26.44  (refer cell H16)

b) Target average time in system (W) = 3 minutes = 3/60 hour = 0.05 hour

For s = 6, W = 0.0286, which is less than target W of 0.05

Therefore, minimum number of voting booths needed to keep the average time in system under three minutes = 6 voting booths

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