$1.2.3.4.5.6.7.8.$ Linear programming problems are solved the fastest by the isoprofit line method. How does it work?a$.$ It determines constraints.b$.$ It defines variable.c$.$ It finds an optimal solution.d$.$ None of the above. All problems of LP seek to maximize or minimize some quantity, usually profit or cost$.$a$.$ Trueb. False An LP problem has a bounded feasible region. If this problem has an equality $1=2$ constraint, thena. this must be a minimization problem.b$.$ the feasible region must consist of a line segment.c$.$ the problem must be degenerate.d$.$ the problem must have more than one optimal solution. Which of the following would cause a change in the feasible region?a$.$ Increasing an objective function coefficient in a maximization problemb. Adding a redundant constraintc. Changing the right$-$hand side of a nonredundant constraintd. Increasing an objective function coefficient in a minimization problemIf a nonredundant constraint is removed from an LP problem, thena. the feasible region will get larger.b$.$ the feasible region will get smaller.c$.$ the problem would become nonlinear.d$.$ the problem would become infeasible. In the optimal solution to a linear program, there are $20$ units of slack for a constraint. From this we know that a$.$ the dual price for this constraint is $20.$b$.$ the dual price for this constraint is $0.$c$.$ this constraint must be redundant.d$.$ the problem must be a maximization problem. What is the essential condition for using the graphical method?a$.$ negative variablesb. integer variablesc. only two decision variablesd. more than three variables In LP$,$ numbers in the objective and constraints are always known and do not change during the period being studied. This assumption is calleda. proportionality.b$.$ additivity. $9.10.11.12.13.14.$ c$.$ divisibility.d$.$ certainty. In LP$,$ variables do not have to be integer valued and may take on any fractional value. This assumption is calleda. proportionality.b$.$ divisibility.c$.$ additivity.d$.$ certainty. In solving a linear program, no feasible solution exists. To resolve this problem we mighta. add another variable.b$.$ add another constraint.c$.$ remove or relax a constraint.d$.$ try a different computer program. If the feasible region gets larger due to a change in one of the constraints, the optimal value of the objective functiona. must increase or remain the same for a maximization problem.b$.$ must decrease or remain the same for a maximization problem.c$.$ must increase or remain the same for a minimization problem.d$.$ cannot change.When alternate optimal solutions exist in an LP problem, thena. the objective function will be parallel to one of the constraints.b$.$ one of the constraints will be redundant.c$.$ two constraints will be parallel.d$.$ the problem will also be unbounded.If a linear program is unbounded, the problem probably has not been formulated correctly. Which of the following would most likely cause this?a$.$ A constraint was inadvertently omitted.b$.$ An unnecessary constraint was added to the problem. c$.$ The objective function coefficients are too large.d$.$ The objective function coefficients are too small. An unfeasible solution to an LP problem solved by a graphical methoda. satisfies all of the problems constraints simultane$-$ously.b$.$ satisfies all of the constraints.c$.$ is a corner point of the feasible region.d$.$ is outside the shaded area.