The Nelson Company has four distribution centers (A, B, C, and D) that require shipments of 20, 30, 40, and 10 units per week, respectively. Its three plants (1, 2, and 3) have monthly capacities of 40, 30, and 30, respectively. Shipping costs (in $) follow.

A) It is not feasible in terms of plant capacities.
B) It is not feasible in terms of satisfying distribution center demands.
C) It is feasible, and the weekly shipping cost is less than $1,600.
D) It is feasible, and the weekly shipping cost is greater than $2,000. What can be said about a plant that ships 40 units from 1 to C, 30 units from 2 to B, 20 units from 3 to A, and 10 units from 3 to D?

Question

The Nelson Company has four distribution centers (A, B, C, and D) that require shipments of 20, 30, 40, and 10 units per week, respectively. Its three plants (1, 2, and 3) have monthly capacities of 40, 30, and 30, respectively. Shipping costs (in $) follow.

A) It is not feasible in terms of plant capacities. 
B) It is not feasible in terms of satisfying distribution center demands. 
C) It is feasible, and the weekly shipping cost is less than $1,600. 
D) It is feasible, and the weekly shipping cost is greater than $2,000. What can be said about a plant that ships 40 units from 1 to C, 30 units from 2 to B, 20 units from 3 to A, and 10 units from 3 to D?

Quizplus · Accepted Answer

To determine feasibility, we must ensure that each plant does not exceed its monthly capacity and that the distribution center demands are met. 
For plant 1, it is shipping 40 units to distribution center C, which is less than its monthly capacity of 40. 
For plant 2, it is shipping 30 units to distribution center B, which is less than its monthly capacity of 30. 
For plant 3, it is shipping a total of 30 units (20 to A and 10 to D), which is less than its monthly capacity of 30. 
Therefore, it is feasible in terms of plant capacities. 
To check if distribution center demands are met, we can sum up the units being shipped to each distribution center: 
Distribution center A: 20 
Distribution center B: 30 
Distribution center C: 40 
Distribution center D: 10 
These exactly match the demand for each distribution center, so it is feasible in terms of satisfying distribution center demands as well. 
Finally, the weekly shipping cost can be calculated by multiplying the shipments with the corresponding shipping costs and adding them up: 
(40 * 14) + (30 * 18) + (20 * 15) + (10 * 19) = $1,870 
Thus, the correct choice is C, and the weekly shipping cost is less than $1,600.

The Nelson Company Has Four Distribution Centers (A, B, C