Consider the following IP problem: Maximum Z= 5x1+x2

subject to
-x1+2x2 <=4
x1-x2 <=4
4x1+ x2 <=12

and
x1 >=0, x2>=0
x1, x2 are integers

a. Solve this problem graphically.
b. Solve the LP relaxation graphically. Round this solution to the nearest integer solution and check whether it is feasible. Then enumerate all the rounded solutions by rounding the solution for the LP relaxation in all possible ways (i. e., by rounding each noninteger value both up and down). For each rounded solution, check for feasibility and, if feasible, calculate Z. Are any of these feasible rounded solutions optimal for the IP problem?

Step-by-step explanation:

The integer points which fall in the common region bounded by the lines are

Since, one of the points is we round it to

If we round up then the point will be which does not fall in the bounded region.

Also and no negative values are considered.

Applying in the values in the LP problem

So, the LP problem is maximum at point .

b

step-by-step explanation:

b

step-by-step explanation:

a difference is the result of subtraction. while each of these expressions has subtraction in it, a difference will be the result when subtraction is the last operation applied in the order of operations for the expression. this means subtraction must be outside of the parenthesis. only b has this.