Joe King has ambitions to be mayor of Williston, North Dakota. Joe has determined the breakdown of the steps to the nomination and has estimated normal and crash costs and times for the campaign as follows (times are in weeks).
Joe is not a wealthy man and would like to organize a 16-week campaign at minimum cost. Write and solve a linear program to accomplish this task.
Let Xi = earliest finish time for activity i
Yi = amount of time activity i is crashed
Min 2000YA + 2000YC + 500YD + 500YE + 2000YF + 5000YG + 6000Y H
s.t. XA ? 0 + (6 ? YA)
XB ? 0 + 3
XC ? XA + (9 ? YC)
XD ? XA + (4 ? YD)
XE ? XB + (2 ? YE)
XF ? XB + (3 ? YF)
XG ? 16
XG ? XC + (5 ? YG)
XG ? XE + (5 ? YG)
XH ? XD + (7 ? YH)
XH ? XF + (7 ? YH)
XH ? 16
YA ? 2
YC ? 3
YD ? 2
YE ? 1
Y F ? 2
YG ? 1
YH ? 2
Xi, Yj ? 0 for all i
Solution: XA = 4, XB = 6, XC = 11, XD = 9, XE = 11, XF = 9, XG = 16, XH = 16,
YA = 2, YC = 2, YD = 0, YE = 0, YF = 0, YG = 0, YH = 0, Total crash cost = $8,000
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