Question

# In the ABC retail store customers arrive at an average 50 per shift. The store manager...

In the ABC retail store customers arrive at an average 50 per shift. The store manager wants to calculate whether he should hire 1, 2, 3 or 4 salespeople.He has deter- mined that average waiting times will be 6 minutes with one salesperson, 3 minutes with two salespeople, 2 minutes with three salespeople, and 1 minute with four salespeople.He has estimated the cost per minute that customer wait at \$1. The cost per salesperson per shift (including fringe benefits) is \$70. How many sales people should be hired?

Given that,

Cost per salesperson, Cs = \$ 70 per shift

Cost of waiting, Cw = \$ 1 per minute

Arrival rate, a = 50 per shift

For Number of salesperson, n = 1, Average waiting time, Wq = 6 minutes

Total cost per shift = n*Cs + a*Wq*Cw = 1*70 + 50*6*1 = \$ 370

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For Number of salesperson, n = 2, Average waiting time, Wq = 3 minutes

Total cost per shift = n*Cs + a*Wq*Cw = 2*70 + 50*3*1 = \$ 290

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For Number of salesperson, n = 3, Average waiting time, Wq = 2 minutes

Total cost per shift = n*Cs + a*Wq*Cw = 3*70 + 50*2*1 = \$ 310

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For Number of salesperson, n = 4, Average waiting time, Wq = 1 minutes

Total cost per shift = n*Cs + a*Wq*Cw = 4*70 + 50*1*1 = \$ 330

Total cost per shift is lowest with 2 salespeople.

Therefore 2 sales people should be hired.

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