Given the following all-integer linear program: (COMPLETE YOURSOLUTION IN EXCEL USING SOLVER AND UPLOAD YOUR FILE. BE SURE THATEACH WORKSHEET IN THE EXCEL FILE CORRESPONDS TO EACH QUESTION BELOW)
Max 15x1 + 2x2
s. t. 7x1 + x2 < 23
3x1 - x2 < 5
x1, x2 > 0 and integer
a. Solve the problem (using SOLVER) as an LP, ignoring theinteger constraints.
b. What solution is obtained by rounding up fractions greaterthan or equal to 1/2? Is this the optimal integer solution?
c. What solution is obtained by rounding down all fractions? Isthis the optimal integer solution? Explain.
d. Show that the optimal objective function value for the ILP islower than that for the optimal LP (Eg. Resolve original problemusing SOLVER with the Integer requirement).
e. Why is the optimal objective function value for the ILPproblem always less than or equal to the corresponding LP's optimalobjective function value? When would they be equal?
