Question

please solve in excel

A computer manufacturing company wants to develop a monthly plan for shipping finished products from three of its manufacturing facilities to three regional warehouses. It is thinking about using a transportation LP formulation to exactly match capacities and requirements. Data on transportation costs (in dollars per unit), capacities, and requirements are given below.

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                                          Warehouse  

Plant                              1          2          3         Capacities

A                               2.41     1.63     2.09         4,000

B                               3.18     5.62     1.74         6,000

C                               4.12     3.16     3.09         3,000

Requirement              8,000   2,000   3,000

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a.   How many variables are involved in the LP formulation?

b.   How many constraints are there in this problem?

c.   What is the constraint corresponding to Plant B?

d.   What is the constraint corresponding to Warehouse 3?

Answer 1

ANSWER:

Given that,

a)

Let “I” represents number of plants and “j” represents number of warehouses.

Where, i = A, B, C and j = 1, 2, 3

Let X_ij represents number of items shipped from plant i to warehouse j.

Number of decision variables = 3 x 3 = 9

b)

As there are capacity constraints for three plants and demand constraint for three warehouses, in total there are 3 + 3 = 6 major constraints. In addition, non negative constraint which assumes that all decision variables are greater than or equal to zero.    

c)

Constraint corresponding to plant B is as follows:

X_B1 + X_B2 + X_B3 < = 6,000

d)

Constraint corresponding to warehouse 3 is as follows:

X_A3 + X_B3 + X_C3 = 3,000