Question

Solve the following problem:

max 3x+y

s.t. 4x+y≤ 8

x+y≥3

x+4y≤8

x,y for all integers

Part i) Is this problem convex ? why?

Part ii)Is (x,y)=(1,4) a feasible solution?

Part iii)Is (x,y)=(1,1) a feasible solution?

Part iv)s (x,y)=(1.5,0.5) a feasible solution?

Part v)What is the value of the objective function that corresponds to each of the previous three solutions?

Part vi)Do each of these three values correspond to a lower bound, upper bound, non or both?

Part vii)If we eliminate the last constraint is the new problem convex?

Part viii) Are the above solutions feasible for relaxation?

Part ix) Are the three objective funds. values lower bounds, upper bounds, none, or both for the relaxation?

Answer 1