Question

9. SunRay Transport Company ships truckloads of grain from three silos to four mills. The supply (in truckloads) and the demand (also in truckloads) together with the unit transportation costs per truckload on the different routes are summarized in the following table. The unit transportation costs are in hundreds of dollars. The model seeks the minimum cost shipping schedule between the silos and the mills. Mill 2 3 4 Supply 220 *11 12 13 14 15 Silo 2 *21 * *23 24 25 14 16 Demand 5 15 15

Answer 1

We can use North West method

supply demand

First, we will select X11 and allocate all the demand of 5 units.

DI =zx o €7X, 2x FIX z mix|o1 15-5=10

Now we will allocate the remaining 10 units of supply to X12

X23 X22 14 16 X32X33X34 15-10=5

Now the demand for column 2 is 5 so we will allocate these units to X22

X23 25-5-20 16 10 X33 X34 15 15

The demand for column 3 is 15 that can be allocated to X23

5 10 12 20-15-5 X24 10 X34

The remaining supply of 5 units in row 2 will be allocated to X24 and the last cell X34 will have the rest allocation

X34 15-5=10