9. A road construction firm seeks to assign its force optimally over the next 28
ID: 364731 • Letter: 9
Question
9. A road construction firm seeks to assign its force optimally over the next 28- . For any number of 10-week periods, working for the state, and earninga . For any number of 6-week periods, working for the county, and earning a . For any number of 3-week periods, working for a private land developer . For any number of weeks, working on parking lot construction, and earning . However, if the firm does any work at all for either the state or county (or week period. They can be assigned to any combination of the following: profit of $3200/week. profit of $2900/week. and earning $2750/week. $2550/week. both), it is expected to contribute $7500 to the campaign fund of a certain anonymous political figureExplanation / Answer
Answer -
Integer Progarmming Mode needs to have the following
The objective function is to maximize the earning by applying the task force for a period of 28 weeks.
The objective function can be with state / country task or without state/country tasks as stateorcountry task involves $7500 campaign funding.
X1 = Stae Task for 10 weeks with $ 3200/week
X2 = Country Task for 6 weeks with $ 2900/week
X3 = Private Task for 3 weeks with $ 2750/week
X4 = Construction Task for any weeks with $ 2550/week
Optimize / maximize : Z1 (with state/country task) = 10X1 + 6X2 + 3X3 + X4 -$7500
Constraints
X1 = 3200 / week
X2 = 2900/week
X3 = 2750/week
X4 = 2550/week
X1 + X2 + X3 + X4 = 28 weeks
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