Question

A company manufactures its products in two plants, one on the east coast of the United States (US) and the other in Europe. It has warehouses for distributing products in the US, Europe and South America. The US plant has a capacity of 10,000 units per month and the Europe plant capacity is 5,000 units per month. Demand in the US is 8,000 units, demand in Europe is 2,000 and demand in South America is 5,000 units. The cost to ship the product from the US to South America is $5.00 per unit, from the US to Europe is $3.00 per unit, from Europe to the US is $3.25 and from Europe to South America $5.50. Cost to ship within a country (i.e. Europe to Europe or US to US) is $1.00 per unit. Find the lowest cost shipping schedule and calculate the transportation cost associated with your schedule. (Just use a heuristic rule. No need to use solver for this problem.)

Answer 1

The lowest cost shipping schedule is to ship 8,000 units from the US to the US and 2,000 units from Europe to Europe, with a total transportation cost of $10,000.

Step-by-step explanation:

To find the lowest cost shipping schedule, we need to compare the costs of shipping from each plant to each destination. Let's calculate the costs for each option:

• Shipping 8,000 units from the US to the US: 8,000 * $1.00 = $8,000
• Shipping 8,000 units from the US to Europe: 8,000 * $3.00 = $24,000
• Shipping 8,000 units from the US to South America: 8,000 * $5.00 = $40,000
• Shipping 2,000 units from Europe to the US: 2,000 * $3.25 = $6,500
• Shipping 2,000 units from Europe to Europe: 2,000 * $1.00 = $2,000
• Shipping 2,000 units from Europe to South America: 2,000 * $5.50 = $11,000

The lowest cost shipping schedule is to ship 8,000 units from the US to the US, and 2,000 units from Europe to Europe. The total transportation cost for this schedule would be $8,000 + $2,000 = $10,000.

Answer 2

To find the lowest cost shipping schedule, consider the demand and capacities of the plants and the shipping costs. The lowest cost schedule is to produce 8,000 units in the US, ship 2,000 units to Europe, and ship 5,000 units to South America, with a total transportation cost of $33,000.

Step-by-step explanation:

To find the lowest cost shipping schedule, we need to consider the demand and capacities of the two plants and the cost of shipping between the locations. The lowest cost schedule can be determined by comparing the total transportation costs for different shipping routes.

First, let's calculate the transportation costs for the given demand and capacities:

• Shipping from US to Europe: $3.00 x 2,000 units = $6,000
• Shipping from US to South America: $5.00 x 5,000 units = $25,000
• Shipping from Europe to US: $3.25 x 8,000 units = $26,000
• Shipping from Europe to South America: $5.50 x 2,000 units = $11,000
• Shipping within US: $1.00 x 2,000 units = $2,000
• Shipping within Europe: $1.00 x 8,000 units = $8,000

Based on these costs, we can see that the lowest cost shipping schedule is to produce 8,000 units in the US, ship 2,000 units to Europe, and ship 5,000 units to South America.

The total transportation cost for this schedule would be $6,000 (from US to Europe) + $25,000 (from US to South America) + $2,000 (within US) = $33,000.