$($a$)$ Write down a linear programming model of the problem to minimize

the sum of shortage and shipping costs.

$($b$)$ Formulate a balanced transportation problem by defining sets of sup

ply and demand points with corresponding values of supply and de

mand as well as the unit costs of shipment.

$($c$)$ Solve the model using transportation simplex algorithm.

$($d$)$ Does the solution vector you got in Part $($c$)$ have integer values?

Is this expected? Can a transportation problem have non$-$integer

optimal solutions? Please explain.