A contractor has one mechanical excavator and one bulldozer, which are available for work on either...

 

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A contractor has one mechanical excavator and one bulldozer, which are available for work on either of two adjacent sites. On one site, clay overburden is being excavated for a ballast pit owner, and on the other, ballast is being removed under subcontract to another client. Experience tells the contractor that $50 profit can be made for 1000 m3 of clay overburden and $60 profit for every 1000 m3 of ballast removed. A comprehensive work study assesses the resources required to remove 1000 m3 of clay to be 8 hours' use of the excavator, 4 hours' use of the bulldozer and 50 man-hours of operatives' time. In the case of the excavation of 1000 m3 of ballast, the resources are required for 4 hours, 5 hours, and 13 man-hours, respectively. The contractor's employees work a 40- hour week. The mechanical equipment is also available for a 40-hour week. In addition to the mechanical equipment, 5 laborers are available for up to 40 hours each in any one week in order to assist with the work. When they are not employed on the excavation, use can be made of the operatives' elsewhere. Write a linear programming formulation for maximizing profit during one working week The unknowns are: X₁ Units of 1000 m3 of clay excavated X2 Units of 1000 m3 of ballast excavated A contractor has one mechanical excavator and one bulldozer, which are available for work on either of two adjacent sites. On one site, clay overburden is being excavated for a ballast pit owner, and on the other, ballast is being removed under subcontract to another client. Experience tells the contractor that $50 profit can be made for 1000 m3 of clay overburden and $60 profit for every 1000 m3 of ballast removed. A comprehensive work study assesses the resources required to remove 1000 m3 of clay to be 8 hours' use of the excavator, 4 hours' use of the bulldozer and 50 man-hours of operatives' time. In the case of the excavation of 1000 m3 of ballast, the resources are required for 4 hours, 5 hours, and 13 man-hours, respectively. The contractor's employees work a 40- hour week. The mechanical equipment is also available for a 40-hour week. In addition to the mechanical equipment, 5 laborers are available for up to 40 hours each in any one week in order to assist with the work. When they are not employed on the excavation, use can be made of the operatives' elsewhere. Write a linear programming formulation for maximizing profit during one working week The unknowns are: X₁ Units of 1000 m3 of clay excavated X2 Units of 1000 m3 of ballast excavated

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Lets define the decision variables for the linear programming problem X1 Units of 1000 m of clay ... View the full answer