Question

18. An appliance manufacturer has two factories located around the world, each with

its own capacity:
• F1 can make 8 appliances per day.
• F2 can make 10 per day.
The factories can deliver to two different distribution centers. Every day each
distribution center must receive 9 appliances each.
The cost to deliver appliances from each factory to each distribution center is
listed in the table below:
Distribution Center 1 Distribution Center 2
$3
$3
F1 $4
F2 $8
Using the factory production constraints and the delivery costs in the above
matrix, what is the lowest cost to deliver all 18 appliances to the distribution
centers?

Answer 1

To minimize the delivery cost, Factory F1 should send all 8 of its appliances to Distribution Center 2 at $3 each, and Factory F2 should send 9 appliances to Distribution Center 1 at $3 each and 1 appliance to Distribution Center 2 at $8. The total minimum cost of delivery is $59.

Step-by-step explanation:

The goal is to find the lowest cost of delivering 18 appliances from factories F1 and F2 to the two distribution centers. Since F1 makes 8 appliances and F2 makes 10 per day, both factories together produce exactly the number of appliances required by the distribution centers, 18 in total. The costs for delivery are:

• F1 to Distribution Center 1: $4
• F1 to Distribution Center 2: $3
• F2 to Distribution Center 1: $3
• F2 to Distribution Center 2: $8

To minimize costs, we want to assign as many appliances as possible from the factory with the cheaper delivery costs to each respective distribution center. Therefore, F1 should deliver all 8 of its appliances to Distribution Center 2 at $3 each, and F2 should deliver 9 appliances to Distribution Center 1 at $3 each, having 1 appliance left to deliver to Distribution Center 2 at $8.

Now let's calculate the total cost:

• F1 to Distribution Center 2: 8 appliances × $3 = $24
• F2 to Distribution Center 1: 9 appliances × $3 = $27
• F2 to Distribution Center 2: 1 appliance × $8 = $8

Total cost = $24 + $27 + $8 = $59