System of Operations

SOM 306

Case Study

1/17/08

Introduction:

BookCase Solutions (BCS) has a current shelf production of two models, Model S and Model LX. In this case analysis I will determine the quantities of the Models that will maximize profit for this manufacturing company, since profit is currently a major concern for their management team. To generate an attainable goal I will use a linear programming model in order to represent the company’s goal, the factors involved, and the limitations put on the process by the constraints.

Linear Programming Model:

The current production level of the company consists of producing and selling 400 units of Model S and 1400 units of Model LX, on a per month basis. The costs incurred for the production of Model S is $1839/unit, but the model is only sold for $1800/unit, which holds a contribution margin of negative $39. The company must decide on the possibility of reducing production for this model, or an alternative to maximize their goal. From the information provided I created an Objective Function, which holds Z= $1800X1+$2100X2; where the dollar amounts represent the current selling price for both Model S and Model LX. The objective function also represents the number of units sold by the variables in the equation. With this function I will be able to find the best possible solution for BCS.

Constraints:

A constraint in the linear programming model is defined as the limitations brought upon by the process of manufacturing the product. In this case, in order to create their shelves they must be subjected to three phases; stamping, forming, and assembly. These phases in the manufacturing process are also the constraints for the model. Each constraint represents the expenses and labor that is necessary per unit. Each constraint must be met in order to satisfy the objective function.

The first constraint is stamping. This constraint is defined by the amount of hours that each model spends in this department. Stamping => 120X1+420X2 <= 540 hours of labor. The limitation of 540 hours is defined in this constraint, and must be met. This constraint is a less than constraint because the maximum amount the model can spend in this department is defined by 120 hours.

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