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(P5-18) A food distribution company ships fresh spinach from its four packing pl

ID: 407546 • Letter: #

Question

(P5-18) A food distribution company ships fresh spinach from its four packing plants to large East-Coast cities. The shipping costs per crate and the supply and demand are shown in the table below.

Formulate a model that will permit the company to meet its demand at the lowest possible cost.

The company wishes to spread out the source for each of its markets to the maximum extent possible. To accomplish this, it will accept a 5% increase in its total transportation cost from part (a). What is the new transportation plan, and what is the new cost?

MARKETS

Packing Plants

Atlanta

Boston

Charlestown

Dover

Supply

Eaglestown

$6.00

$7.00

$7.50

$7.50

8,000

Farrier

$5.50

$5.50

$4.00

$7.00

10,000

Guyton

$6.00

$5.00

$6.50

$7.00

5,000

Hayesville

$7.00

$7.50

$8.50

$6.50

9,000

Demand

8,000

9,000

10,000

5,000

MARKETS

Packing Plants

Atlanta

Boston

Charlestown

Dover

Supply

Eaglestown

$6.00

$7.00

$7.50

$7.50

8,000

Farrier

$5.50

$5.50

$4.00

$7.00

10,000

Guyton

$6.00

$5.00

$6.50

$7.00

5,000

Hayesville

$7.00

$7.50

$8.50

$6.50

9,000

Demand

8,000

9,000

10,000

5,000

Explanation / Answer

Answer:

Notes:

1. Find out minimum cost and allot maximum quantity for that minimum cost.

2. Minimum cost is $4 for Farrier against Charlestown((10,000 units), next minimum cost is $5 for Guyton against Boston(5,000 units), next minimum cost is $6 for Eaglestown against Atlanta(8,000 units), and remaining for Hayesville (4,000 units against Boston @ $7.5 and 5,000 units against Dover @ $6.5)

3. Alternatively we can form matrix to solve above.

Total Cost:

Transportation plan will remain same as it increases cost of each plant with each market by 5%. In this case total cost would be $175,500 +5% = $184,275.00

Packing Plants Atlanta Boston Charlestown Dover Supply Eaglestown 8000 8,000 Farrier 10000 10,000 Guyton 5000 5,000 Hayesville 4000 5000 9,000 Demand 8,000 9,000 10,000 5,000