Q1) let
X1 be number of type 1
X2 be number of type 2
X3 be number of type 3
X4 be number of type 4
Objective function
Maximize
Z = 5x1 + 22x2 + 3x4
Subject to
Number of 25% of the unit
X3 + x4
X3 + x4 ………………………….1
1 + 13700x2 + 10200x3 = 7900x4)
111.15x1 + 89.05x2 + 66.3x3 +51.35x4 …………………………2
175x1+ 145x2 + 100x3 + 110x4 ……………………………………….3
X1 + x2 + x3 + x4 …………………………………………………………………..4
230x1 + 200x2 + 135x3 = 125x4 …………………………………………5
- b) From the excel file
optimal solution is 154
Q2)
Arrival time = λ = 17
Service rate =
Formula for waiting time
Wq =
=
= 3.44 hours
Thus the waiting time is 3.44 hours hence NO
- b)
Required waiting time
Lq =
Here k is the number of of services improving quality which is 2
Lq =
= 0.374
Required waiting time on the line is
Wq =
= 0.374/17
= 0.022 hours
Strategy
Hire a second person to operate a second checkout counter. The two-checkout counter operation would have a service rate of 21 customers per hour for each checkout counter.
Q4)
Required salary = $35
Number of employees during 0hr – 4hr
X1
Number of employees during 4hr – 8hr
X1 + x2
Number of employees during 8hr – 12hr
X1 + x2 + x3
Number of employees during 12hr – 16hr
X1 + x2 + x3 + x4
Number of employees during 16hr – 20hr
X1 + x2 + x3 + x4 + x5
Number of employees during 20hr – 24hr
X1 + x2 + x3 + x4 + x5 +x6
- b) From the excel
the total is 1435
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