A product is produced at three plants P1 P2 and P3 and shipp

A product is produced at three plants (P1, P2 and P3) and shipped to three warehouses (W1, W2 and W3). The plant capacities are as follows: P1- 300, P2- 500, P3- 100. Warehouse demands are as follows: W1 - 200, W2- 400, W3- 300. The transportation costs per unit are the following: P1 to W1 $20, P1 to W2 $16, P1 to W3 $24; P2 to W1 $10, P2 to W2 $10, P2 to W3 $8; P3to W1 $12, P3 to W2 $18, P3 to W3 $10.

a. Determine the minimum cost shipping assignment.

b. Determine the minimum cost.

c. Carefully state your solution.

Solution

Comparing these we select first the least cost i.e. 8 from p2 to w3 This should be maximum used

Hence 300 units of p2 should be sent to w3.

Balance 200 units will be in p2.

Next to 8, the least cost is 10. p2 to w1 or p2 to w2.

But select p2 to w2 because alternate cost 12 is less than 18.

Hence 200 units in p2 to w2.

next p3 to w1 200 units.

Optmal allocation is

Minimum cost is shown below:

Thus under optimal allocation minimum cost = 10800 dollars.