Answer to Question #155105 in Operations Research for Wachira Ann Wangari

Question

Best sell LTD has decided to launch a new product in addition to it's range of products. The following information is provided.

1) The New product may be distributed through any combination of the two company warehouse W1 and W2

2) The available monthly production capabilities for the new products are;

1000 units at plant A

2000 units at plant B

1000 units at plant C

3) Three major concentration points of customer demands are at location E,F qand G which are estimated to have a monthly demand of :

900 units at plant E

800 units at plant F

900 units at plant G

4) The unit production costs amount to sh30, sh40, sh 10 at A, B and C.

5) The unit transportation costs from plant to warehouse and unit delivery cost from warehouse to customer as shown below

Transportation cost schedule

Plants. W1. W2

Sh sh

A. 60. 60

B. 50. 50

C. 130. 40

Delivery cost schedule

Warehouse. E. F. G

Sh sh. Sh

W1. 30 60. 80

W2. 5-. 50 90

Answer 1

Table of shipping costs (optimal):

E F G

A 90 110 140

B 80 100 130

C 70 90 120

Table of shipping units:

E F G Supply

A $x_{11}$ $x_{12}$ $x_{13}$ 1000

B $x_{21}$ $x_{22}$ $x_{23}$ 2000

C $x_{31}$ $x_{32}$ $x_{33}$ 1000

Demand 900 800 900

Constraints for supply:

$x_{11}+$$x_{12}+$$x_{13}\leq1000$

$x_{21}+$$x_{22}+$$x_{23}\leq2000$

$x_{31}+$$x_{32}+$$x_{33}\leq1000$

Constaints for demand:

$x_{11}+$$x_{21}+$$x_{31}\geq900$

$x_{12}+$$x_{22}+$$x_{32}\geq800$

$x_{13}+$$x_{23}+$$x_{33}\geq900$

We use Northwest Corner Method:

E F G Supply

A $x_{11}$ $x_{12}$ $x_{13}$ 1000

B $x_{21}$ $x_{22}$ $x_{23}$ 2000

C $x_{31}$ $x_{32}$ $x_{33}$ 1000

Demand 900 800 900

We begin at the most northwest variable (upper left corner). This is $x_{11}$

we set $x_{11}=min\{supply A,demandE\}=min\{1000,900\}=900$

now demand $E=900-900=0$ , supply $A=1000-900=100$

now the most northwest variable is $x_{12}$

set $x_{12}=min\{supply A,demandF\}=min\{100,800\}=100$

now demand $F=800-100=700$ , supply $A=100-100=0$

now the most northwest variable is $x_{22}$

set $x_{22}=min\{supply B,demandF\}=min\{2000,700\}=700$

now demand $F=700-700=0$ , supply $B=2000-700=1300$

now the most northwest variable is $x_{23}$

set $x_{23}=min\{supply B,demandG\}=min\{1300,900\}=900$

No cells are available, so we are finished.

So, we get:

$x_{11}=900, x_{12}=100, x_{22}=700, x_{23}=900$

So, minimum of total shipping cost:

$90x_{11}+100x_{12}+100x_{22}+130x_{23}=$

$=90\cdot900+100\cdot100+100\cdot700+130\cdot900=278000$