**Kindly solve all questions using QM for Windows

Question 1 [10 marks]

HarryTech Corporation is a global distributor of electrical parts and components. Its customers are electronics companies in the United States, including computer manufacturers and audio/visual product manufacturers. The company contracts to purchase components and parts from manufacturers in Russia, Eastern and Western Europe, and the Mediterranean, and it has them delivered to warehouses in three European ports, Gdansk, Hamburg and Libson. The various components and parts are loaded into containers based on demand from U.S. customers. Each port has limited fixed number of containers available each month. The containers are then shipped overseas by container ships to the ports of Norfolk, Jacksonville, New Orleans, and Galveston. From these seaports the containers are typically coupled with trucks and hauled to inland ports in Front Royal (Virginia), Kansas City and Dallas. There are a fixed number of freight haulers available at each port each month. These inland ports are sometimes called freight villagers, or intermodal junctions ,where the containers are collected and transferred from one transport mode to another (i.e., from truck to rail or vice-versa). From the inland ports, the containers are transported to HarryTechs distribution centers in Tucson, Pittsburgh, Denver, Nashville and Cleveland. Following are the handling and shipping costs ($/container) between each of the embarkation and destination points along this overseas supply chain and the available containers at each port:

European Port	U.S. Port				Available Containers
	4. Norfolk	5. Jacksonville	6. New Orleans	7. Galveston
Gdansk	$1725	1800	2345	2700	125
Hamburg	1825	1750	1945	2320	210
Lisbon	2060	2175	2050	2475	160

U.S. Port	Inland Port			Intermodal Capacity (containers)
	8. Dallas	9. Kansas City	10. Front Royal
4. Norfolk	$825	545	320	85
5. Jacksonville	750	675	450	110
6. New Orleans	325	605	690	100
7. Galveston	270	510	1050	130
Intermodal Capacity(containers)	170	240	140

Inland Port	Distribution Center
	11. Tucson	12. Denver	13. Pittsburgh	14. Nashville	15. Cleveland
8. Dallas	$450	830	565	420	960
9. Kansas City	880	520	450	380	660
10. Front Royal	1350	390	1200	450	310
Demand	85	60	105	50	120

Determine the optimal shipments from each point of embarkation to each destination along this supply chain that will result in the minimum total shipping cost.

Question 2 [5 marks]

An analyst has kept track of the number of defectives produced by five workers on five different machines. The results are shown below for a run of 400 units per machine:

Worker	Machine
	A	B	C	D	E
1	9	7	4	6	2
2	7	4	5	2	1
3	3	4	3	2	3
4	9	7	8	6	5
5	0	3	2	4	3

1. Determine a set of assignments that will minimize the total number of errors for a given run size.
2. What is the total number of defectives expected for the optimal assignment?
3. If another machine was available and number of defectives produced by the five workers for a runoff 400 units was 4, 4, 2, 3, and 1 respectively. Determine the new set of assignments that will minimize the total number of expected defectives.
4. Which machine will not be used?