A firm has prepared the following binary integer program toevaluate a number of potential locations for new warehouses. Thefirm’s goal is to maximize the net present value of their decisionwhile not spending more than their currently available capital.
Max 20x1 + 30 x2 + 10x3 + 15x4
s.t. 5x1 + 7x2 + 12x3 + 11x4 ? 21 {Constraint 1}
x1 + x2 + x3 + x4 ? 2 {Constraint 2}
x1 + x2 ? 1 {Constraint 3}
x1 + x3 ? 1 {Constraint 4}
x2 = x4 {Constraint 5}
x j ={ 1, if location j is selected 0, otherwise xj=1, iflocation j is selected0, otherwise
Solve this problem to optimality and answer the followingquestions:
A. What is the net present value of the optimal solution? (Roundyour answer to the nearest whole number.)
B. How much of the available capital will be spent (Hint:Constraint 1 enforces the available capital limit)? (Round youranswer to the nearest whole number.)
