Question 4: Transportation, Assignment and Transhipment problems [30]

4.1. The three plants that process and pack potatoes are coordinated from a central office that facilitates delivery of sack of potatoes to the mentioned towns/cities. The cost of transporting a sack of potatoes per unit (i.e. 7kg potatoes sack) from each plant to each town/city is shown below. Moreover, the numbers of units of potatoes available from each plant as well as the number of requested units of potatoes at each city/town are provided in the table below.

	Destination 1	Destination 2	Destination 3	Destination 4	Supply
Plant 1	$8	$11	$16	$16	50
Plant 2	12	$5	$8	$8	80
Plant 3	$14	$6	$7	$7	120
Demand	90	70	40	50	250/250

Formulate the linear programming model (i.e. objective function) and the corresponding constraints including the lower bounds of the decision variables.

How many shipments must be made from each plant to each different town/city so that the cost can be minimized