Table 11.11
The Neale Company has four distribution centers (A,B,C,and D)that require monthly shipments of 30,000,24,000,36,000,and 24,000 gallons of diesel fuel per month,respectively.Three wholesalers (1,2,and 3)are willing to supply up to 36,000,48,000 and 30,000 gallons,respectively.Total costs (in $)for both shipping and price per gallon follow.A transportation method tableau is provided below.
-Use the information in Table 11.11.What can be said about a plan that ships 30,000 gallons from 1 to A;6,000 gallons from 1 to C;24,000 gallons from 2 to B;24,000 gallons from 2 to D;and 30,000 gallons from 3 to C?

Question

Table 11.11
The Neale Company has four distribution centers (A,B,C,and D)that require monthly shipments of 30,000,24,000,36,000,and 24,000 gallons of diesel fuel per month,respectively.Three wholesalers (1,2,and 3)are willing to supply up to 36,000,48,000 and 30,000 gallons,respectively.Total costs (in $)for both shipping and price per gallon follow.A transportation method tableau is provided below. 
-Use the information in Table 11.11.What can be said about a plan that ships 30,000 gallons from 1 to A;6,000 gallons from 1 to C;24,000 gallons from 2 to B;24,000 gallons from 2 to D;and 30,000 gallons from 3 to C?

Quizplus · Accepted Answer

The plan ships the required amount of fuel to each distribution center and does not exceed the capacities of the wholesalers. To calculate the total cost, we need to add the costs of shipping and the cost per gallon for each shipment. 
The total cost of shipping 30,000 gallons from 1 to A is (30,000 x 0.25) + 1,000 = $8,000 
The total cost of shipping 6,000 gallons from 1 to C is (6,000 x 0.25) + 1,000 = $2,500 
The total cost of shipping 24,000 gallons from 2 to B is (24,000 x 0.20) + 2,000 = $6,800 
The total cost of shipping 24,000 gallons from 2 to D is (24,000 x 0.20) + 2,000 = $6,800 
The total cost of shipping 30,000 gallons from 3 to C is (30,000 x 0.15) + 3,000 = $7,500 
The total cost for this plan is $8,000 + $2,500 + $6,800 + $6,800 + $7,500 = $31,600, which is less than or equal to $260,000. Therefore, the plan is feasible and the total monthly cost is less than or equal to $260,000.

Table 11.11 The Neale Company Has Four Distribution Centers (A,B,C,and D)that Require