Linear programming

 

Acme Manufacturing makes a variety of household appliances at a single manufacturing facility. The expected demand for one of these appliances during the next 4 months is shown in the following table along with the expected production costs and the expected capacity for producing these items.

Month

1

2

3

4

Demand

420

580

310

540

Production Cost

$49.00

$45.00

$46.00

$47.00

Production Capacity

500

520

450

550

Acme estimates it costs $1.50 per month for each unit of this appliance carried in inventory at the end of each month. Currently, Acme has 120 units in inventory on hand for this product. To maintain a level workforce, the company wants to produce at least 400 units per month. They also want to maintain safety stock of at least 50 units per month (minimum inventory at the end of the month). Acme wants to determine how many of each appliance to manufacture during each of the next 4 months to meet the expected demand at the lowest possible total cost.

Provide the complete linear programing formulation. Clearly specify decision variables, objective function and constraints.
Build a model in Excel and paste a screenshot here. Use “FORMULATEXT” in your model to show calculations.
According to Excel Solver, what is the optimal production plan for Acme Manufacturing? What is the minimum total cost?
Use SolverTable to investigate the effect on the total cost of changes in the initial inventory from 0 units to 120 units in increments of 20.

 

 

Sample Solution

lished in the Treaty of Maastricht and is determined on the basis of an individual holding the nationality of a Member State: Article 9 of the Treaty on European Union (TEU) defines EU citizenship as “Every person holding the nationality of a Member State shall be a citizen of the Union. Citizenship of the Union shall be additional to and not replace national citizenship.” Article 20 (2) of the Treaty on the Functioning of the European Union (TFEU) sets out the rights which EU citizens are entitled to and under Article 21 (1) TFEU, EU citizens have the right to move and reside freely in other Member States. Directive 2004/38 which is also known as the Citizens Rights Directive, was enacted in April 2004 and also covers the right of EU citizens and their family members rights to move and reside freely within other Member States. In order to determine the parties rights, it is necessary to determine whether they are EU citizens first and then analyse how EU law relates to their situations.

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