PLEASE ANSWER TRUE OR FALSE FOR THE FOLLOWING STATEMENTS: $1.$ To develop an LP mathematical model for a transportation or transshipment problem, you must define a variable for each arc and a constraint for each node. $2.$ A transportation problem with $3$ sources and $4$ destinations will have $12$ variables in the objective function. $3.$ A dummy origin in a transportation problem is used when demand is less than supply. $4.$ Generally, the optimal solution to an integer linear program is NOT sensitive to the constraint coefficients than is a linear program. $5.$ The constraint x$1-$x$2=0$ implies that if project $1$ is selected, project $2$ cannot be$.6.$ If Project $5$ must be completed before Project $6,$ the constraint would be x$5=>$ x$6.$