Question

Green Valley Mills produces carpet at plants in St. Louis and Richmond. The carpet is then shipped to two outlets, located in Chicago and Atlanta. The cost per ton of shipping carpet from each of the two plants to the two warehouses is as follows:

To(cost)




From Chicago Atlanta




St louis $40 $65




Richmond 70 30






The plant at St. Louis can supply 250 tons of carpet per week; the plant at Richmond can supply 400 tons per week. The Chicago outlet has a demand of 300 tons per week, and the outlet at Atlanta demands 350 tons per week. The company wants to know the number of tons of carpet to ship from each plant to each outlet in order to minimize the total shipping cost. Solve this transportation problem.

Answer 1

49250

Step-by-step explanation:

Calculation through North West corner Method:

From Chicago Atlanta Supply

St. Louis 40 65 250

Richmond 70 30 400

Demand 300 350 -

The matrix is balance matrix because demand is equals to supply.

In first step of North West corner method:

We supply 250 units to the Chicago for St. Louis is 40.

We supply 50units to the Chicago for Richmond is 70.

We supply 350units to the Chicago for Richmond is 30.

We supply 350units to the Chicago for Richmond is 30.

Calculation for the degree of freedom is:

=

Raw

total

+

Colum

total

−

1

=

2

+

2

−

1

=

4

Now introduce the

θ

on that value where the lope is note created and the value is 65:

The calculation for the cost is:

=

250

×

65

+

300

×

70

+

400

×

30

=

49250