# Solved > 123) A company has determined the “demand points”:1909794 …

123) A company has determined the “demand points” and their relative locations as follows:

 Demand Points X Coordinate Y Coordinate Load A 12 15 1000 B 22 9 450 C 16 14 750 D 14 15 550 Total Load 2750

If a company desires to locate a manufacturing facility at the center of gravity, what would be the x and y coordinates of the facility?

124) The operations manager has narrowed down the search for a new plant to three locations. Fixed and variable costs follow.

Plot the total cost curves in the chart provided and identify the range over which each location would be best. Then use break-even analysis to calculate exactly the break-even quantity that defines each range.

a. What is the break-even quantity between A and B?

b. What is the break-even quantity between B and C?

125) Consider the transportation tableau shown below. What is the minimum cost of transporting the production from Ada, Bugtussle, and Choctaw to Durant, Edmond, and Foss if costs per unit are shown at the intersections of each location?

 Durant Edmond Foss Capacity Ada 5 7 3 200 Bugtussle 3 4 4 300 Choctaw 8 6 8 200 Requirements 250 300 150

126) A national firm has beef jerky processing facilities in Locations 1, 2, 3, and 4. They ship to central distributors (represented as A, B, C, and D) handling four regions of the country. The per-unit shipping costs between each possible combination of locations are shown in the following table.

 A B C D 1 \$5 \$10 \$5 \$4 2 \$3 \$4 \$4 \$3 3 \$8 \$6 \$8 \$2 4 \$2 \$3 \$5 \$9

The processing facility locations are capable of monthly production (in tons) as follows:

Location 1: 600

Location 2: 350

Location 3: 475

Location 4: 850

The central distributors have firm commitments for the following quantities:

Distributor A: 650

Distributor B: 725

Distributor C: 400

Distributor D: 500

What is the lowest-cost shipping arrangement that can be made between the plant locations and distributors and what is the annual shipping cost?

127) Five sources exist for the civet cat coffee favored by true coffee connoisseurs. The four processing centers for these coffee beans are scattered about the country, each with a different level of demand. The five sources all face different cost structures for transporting their beans, the prices in the table reflect a dollar cost per 50 pound bag of coffee beans. The total amounts supplied by each source and demanded by each destination are also shown in the table, and as luck would have it, the total supply equals the total demand. What is the optimal shipping scheme such that the total transportation cost is minimized?

 Destination 1 Destination 2 Destination 3 Destination 4 Supply Source 1 \$5 \$7 \$2 \$9 400 Source 2 \$8 \$6 \$3 \$4 400 Source 3 \$11 \$15 \$18 \$11 300 Source 4 \$9 \$6 \$4 \$3 200 Source 5 \$7 \$9 \$11 \$8 200 Demand 500 350 250 400 1500

128) As legend has it, Buddhist monks trained monkeys to gather the youngest leaves from the tops of wild tea trees. The deft, monkey -picked leaves are unbroken and evenly sized to create the finest oolong tea in the world. There are five plantations that use monkeys for this task and four tea centers where the leaves must be shipped. The cost to send a kilogram of leaves from each plantation to each tea center is shown in the table. Note that supply equals demand in this scenario. What is the optimal shipping scheme such that the total transportation cost is minimized?

 Tea House 1 Tea House 2 Tea House 3 Tea House 4 Supply Monkey 1 \$12 \$13 \$23 \$15 400 Monkey 2 \$6 \$17 \$11 \$4 400 Monkey 3 \$6 \$14 \$13 \$19 300 Monkey 4 \$8 \$10 \$6 \$8 200 Monkey 5 \$21 \$22 \$5 \$21 200 Demand 500 350 250 400 1500

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