A product is produced by four factories F1, F2, F3, and F4. Their production capacities are: F1:47 units, F2:67 units, F3:27 units and F4:57 units. These factories supply the product to four stores, demand of which is 22, 32, 102, and 17 units respectively. Unit transportation cost in dollars from each factory to each store is given in the following table. Determine the extent of deliveries from each of the factories to each of the stores so that the total production and transportation cost is minimum. Factories Stores Supply   S1 S2 S3 S4   F1 4 6 8 13 47 F2 14 12 10 8 67 F3 11 1 7 10 27 F4 10 12 14 9 57 Demand 22 32 102 17

2.) Your business provides technical support for very complex and specialized machinery used by companies throughout the country, and you currently have support centers at 5 locations. However, due to a poor market, you have been forced to close your centers in Houston and San Diego. You will have to relocate all of your technicians in these two centers to your other three centers in Cleveland, Seattle, and Charlotte. Due to the varying costs of living in each city, and travel and retraining times, the cost for relocating an employee varies depending on where the employee is moving. These costs are given in the following table: To: From: Cleveland Seattle Charlotte $5,000 | $7,000 $7,000 $4,000 $6,000 $8,000 Houston San Diego You currently have 40 employees in Houston and 55 employees in San Diego, which all need to be relocated. Cleveland is able to take in at most 35 relocated employees, Seattle can take in at most 32 employees, and Charlotte is able to take in at most 50 employees.…

Waikato Farm Machinery Ltd (‘WFML’), is a well- established business, with the main base of its operations in Te Rapa, Hamilton. Its business is the importation and distribution of farm machinery such as tractors, loaders, diggers, bulldozers as well as farming equipment such as disc ploughs, rotovators, grain silos including machinery used by dairy farmers in milking sheds. The imported equipment is then sold at wholesale prices to smaller businesses in other centres in the Waikato and King Country regions, that on sell them to farmers. WFML has developed a formidable reputation as a supplier of such goods for at least two reasons. First, it imports machinery and equipment of the highest quality such as John Deere tractors from the United States and International Harvester tractors from Germany. Secondly, it has consistently stood by the goods it sells and efficiently attends to any difficulties experienced by retailers such as the repair of any defects. More importantly it is able to…