Green Valley Mills produces carpet at plants in (1)St. Louis, (2)Richmond, and (3)Nashville. The carpet is then shipped to four outlets, located in (1)Chicago, (2)Atlanta, (3)Dallas, and (4)Pittsburgh. The cost per ton of shipping carpet from each of the three plants to the four outlets, plant capacity, and demand required at each outlet are as follows:

From/To	1	2	3	4	Supply Available
St. Louis	$500	$750	$300	$450	20 tons
Richmond	$650	$800	$400	$600	17 tons
Nashville	$400	$700	$500	$550	18 tons
Demand Required	10 tons	11 tons	13 tons	14 tons

Please formulate a linear programming model by defining the decision variables, objective function, and constraints, which will be used to help Green Valley determine the best amount of carpet shipped from each plant to each outlet in order to minimize the total transportation cost.

What is the total transportation cost for the problem? You can address this Linear Programming problem in the following separate steps.

QD1. Please clearly define all decision variables.

QD2. Using the variables defined, please give the objective function.

QD3. Please give the constraints for the problem.

QD4. Please solve this linear programming problem using Excel solver or QM-for-Windows What would be the optimal transportation plan, and the total transportation cost?