WHAT ARE THE CONSTRAINTS FOR SOLVER? Allied Freight supplies goods to three cust

Question

WHAT ARE THE CONSTRAINTS FOR SOLVER?

Allied Freight supplies goods to three customers, who each require 30 units. The company has two warehouses. In warehouse 1, 40 units are available, and in warehouse 2, 30 units are available. The costs of shipping one unit from each warehouse to each customer are shown below. There is a penalty for each unsatisfied customer unit of demand – with customer 1, a penalty cost of $90 is incurred; with customer 2, $80; and with customer 3, $110.

To

Customer 1

Customer 2

Customer 3

From

Warehouse 1

$15

$35

$25

Warehouse 2

$10

$30

$40

Penalty cost

$90

$80

$110

To

Customer 1

Customer 2

Customer 3

From

Warehouse 1

$15

$35

$25

Warehouse 2

$10

$30

$40

Penalty cost

$90

$80

$110

Explanation / Answer

Here there are 6 decision variables, Xij for i = 1, 2 representing the warehouses and for j = 1,2 and 3 representing the customers. Here each customer has to have 30 units but and each of the warehouse has some fixed capacities. Therefore there would be 3 constraints, one for each customer and 2 constraints, one for each warehouses. Therefore we get the constraints as:

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