$1.$ Whenever total supply is less than total demand in a transportation problem, the LP model does not determine how the unsatisfied demand is handled.

a$.$ True

b$.$ False

$2.$ A transportation problem with $3$ sources and $4$ destinations will have $7$ decision variables.

a$.$ True

b$.$ False

$3.$ If a transportation problem has four origins and five destinations, the LP formulation of the problem will have nine constraints.

a$.$ True

b$.$ False

$4.$ A dummy origin in a transportation problem is used when supply exceeds demand.

a$.$ True

b$.$ False

$5.$ Transshipment problem allows shipments both in and out of some nodes while transportation problems do not.

a$.$ True

b$.$ False

$6.$ The number of units shipped from origin i to destination j is represented by

a$.$ xij.

b$.$ xji.

c$.$ cij.

d$.$ cji.

$7.$ The assignment problem is a special case of the

a$.$ transportation problem.

b$.$ transshipment problem.

c$.$ maximal flow problem.

d$.$ shortest$-$route problem.

$8.$ Which of the following is not true regarding the linear programming formulation of a transportation problem?

a$.$ Costs appear only in the objective function.

b$.$ The number of variables is $($number of origins$)$ x $($number of destinations$).$

c$.$ The number of constraints is $($number of origins$)$ x $($number of destinations$).$

d$.$ The constraints' left$-$hand side coefficients are either $0$ or $1.$

$9.$ The objective of the transportation problem is to

a$.$ identify one origin that can satisfy total demand at the destinations and at the same time minimize total shipping cost.

b$.$ minimize the number of origins used to satisfy total demand at the destinations.

c$.$ minimize the number of shipments necessary to satisfy total demand at the destinations.

d$.$ minimize the cost of shipping products from several origins to several destinations.

$10.$ The assignment problem constraint x$3$i $+$ x$32+$ x$33+$ x$34<=2$ means

a$.$ agent $3$ can be assigned to $2$ tasks.

b$.$ agent $2$ can be assigned to $3$ tasks.

c$.$ a mixture of agents $1,2,3,$ and $4$ will be assigned to tasks.

d$.$ there is no feasible solution.