A company wants to build a new factory in either Atlanta or Columbia.It is also considering building a warehouse in whichever city is selected for the new factory.The following table shows the net present value NPV)and cost of each facility.The company wants to maximize the net present value of its facilities,but it only has $16 million to invest.
Variable Decision
NPV
$million)
Cost $million)
^X₁Factory in Columbia 3 10
^X₂Factory in Atlanta 4 8
^X₃Warehouse in Columbia 2 6
^X₄Warehouse in Atlanta 1 5
Based on this ILP formulation of the problem what is the optimal solution to the problem?
MAX: ^{3 X}₁^{+ 4 X}₂^{+ 2 X}₃^{+ X}₄
Subject to: ^{10 X}₁^{+ 8 X}₂^{+ 6 X}₃^{+ 5 X}₄^{≤ 15}
X₁+ X₂= 1 X₃+ X₄≤ 1 X₃− X₁≤ 0 X₄− X₂≤ 0 X_i= 0,1

Question

Quizplus · Accepted Answer

The Answer of A company wants to build a new factory in either Atlanta or Columbia.It is also considering building a warehouse in whichever city is selected for the new factory.The following table shows the net present value NPV)and cost of each facility.The company wants to maximize the net present value of its facilities,but it only has $16 million to invest. Variable Decision NPV $million) Cost $million) ^X₁Factory in Columbia 3 10 ^X₂Factory in Atlanta 4 8 ^X₃Warehouse in Columbia 2 6 ^X₄Warehouse in Atlanta 1 5 Based on this ILP formulation of the problem what is the optimal solution to the problem? MAX: ^{3 X}₁^{+ 4 X}₂^{+ 2 X}₃^{+ X}₄ Subject to: ^{10 X}₁^{+ 8 X}₂^{+ 6 X}₃^{+ 5 X}₄^{≤ 15} X₁+ X₂= 1 X₃+ X₄≤ 1 X₃− X₁≤ 0 X₄− X₂≤ 0 X_i= 0,1

A Company Wants to Build a New Factory in Either