Question

The Medequip Company produces precision medical diagnostic equipment at two factories. Three medical centers have placed orders for this month’s production output. The table shows what the cost would be for shipping each unit from each factory to each of these customers. Also shown are the numbers of units that will be produced at each factory and the number of units ordered by each customer.



A decision now needs to be made about the shipping plan for how many units to ship from each factory to each customer.
• Formulate a linear programming model for this problem.

Answer 1

An organization needs to use its resources effectively in order to reach the objectives. This is possible when the organization can identify the constraints in maximize their profits or minimize losses.

Linear programming is used to develop the relationship between the objective of organization and constraints of resources.

Consider the following information:

Shipping from factory to customer is as follows:

Develop a linear programming problem as follows:

In transportation, the objective is to minimize cost. The output from the source should meet the demand at the destinations.

Develop a formulated spreadsheet as follows:

Enter the constraints, decision variables and objective function in solver as follows:

The output is as follows:

Therefore, the total cost is $540,000.

The shipment from Factory 1 should be 200 units for customer 2 and 200 units from customer 3.

The shipment from factory 2 should be 300 units for customer 1 and 200 units from customer 3.

Transportation model:

In organizations, material procurement and distribution of products is very important. If the transportation of products is not controlled, the transportation costs will increase. To avoid the excess costs, Organizations use different techniques.

Transportation model is a linear programming method which helps to minimize the costs involved in transportation of material between different sources and destinations.

It can also be solved by transportation model using the spreadsheet as follows:

Enter the values in excel as follows:

The output is as follows:

Hence, the cost of shipping is $540,000.