please give simple justification thanks 4. True or False True or false. For each of the following statements, circle T if it is true, circle F if it is false. No justifications required. The following is a Linear Program. F T F min T F T F subject to The following is a Linear Program. X1 subject to - 2x2 2 2x1 + 3x2 5 X1 0 X2 3 max + x2 + x3 2x1 + x2x3 1 X1X2 2 T F Consider the following Linear Program with decision variables x and 2. Here, 3 is a parameter, a fixed but unknown number. max 1 + x subject to x1 + 2x B X1 0 X2 0 If we increase the value of 3, then the value of this Linear Program does not decrease. An Integer Program can have infinitely many optimal solutions. A Linear Program can have infinitely many optimal solutions.

4. True or False True or false. For each of the following statements, circle T if it is true, circle F if it is false. No justifications required. T F The following is a Linear Program. min2x12x2subjectto2x1+3x25x10x23 T F The following is a Linear Program. maxx1+x2+x3subjectto2x1+x2x31x1x22 T F Consider the following Linear Program with decision variables x1 and x2. Here, is a parameter, a fixed but unknown number. maxx1+x2subjecttox1+2x2x10x20 If we increase the value of , then the value of this Linear Program does not decrease. T F An Integer Program can have infinitely many optimal solutions. T F A Linear Program can have infinitely many optimal solutions