6 . Consider the following all-integer linear program:

Max 10x_1+3x_2

s.t.

6x_1+7x_2 40

3x_1+1x_2 11

x1,x2 0 and integer

The value of the optimal solution to the LP Relaxation is _____ and it is given by x1 = _____, x2 = _____ Since we have all less-than-or-equal-to constraints with positive coefficients, the solution obtained by rounding down the values of the variables in the optimal solution to the LP Relaxation is feasible. The solution obtained by rounding down is x1 = _____, x2 = _____ with value _____. Thus a lower bound on the value of the optimal solution is given by this feasible integer solution with value _____. An upper bound is given by the value of the LP Relaxation, _____. (Actually an upper bound of ____ could be established since no integer solution could have a value between ____ and ____.)

Please provide a detailed answer, following the steps of the problem. Thank you!