Project

Soukpafolo Ismael Kone

Steven Carnovale

ISQA410

                                    Case Study #2 (Rougir)

1. What are the costs for producing the three products in-house?

Raw material costs:

        Purified water: 1$ per pound

        Oil: 1.50$ per pound

        Color and scent: $3 per pound        

Emulsifiers: $2 per pound

Labor costs:

        First shift ($8.50/hour)

                Stage1: $8.50 per hour

                 Stage2: $9.25 per hour

        Second shift 10% reduction in capacity and a 10% increase in wage rate

                Stage 1: (0.1*8.50) – 8.50 = $7.65        

Stage 2: (0.1*9.25) – 9.25 = $8.325

1. Develop a linear programming model for this problem.

Since the company seeks to minimize the expenses, let’s Z be the objective function

The linear programming model for this problem can be describe as:

Z = (cost of labor + cost of raw material) (F + B + C)

Decision variables:

F: number of units of face cream

B: number of units of body cream

H: number of units of hand cream

Subject to constraints are:

1.5F + 1.8B + H

0.8F + 6B + 0.5H

8F + 6B + 7H

F + 3B + 2H

0.5F + 0.3B + 0.4H

0.5F + 0.7F + 0.6H

F >= 12000

B >= 8000

H >= 18000

AND F,B,H >= 0

What production schedule minimizes total cost including outsourcing, and what is the corresponding  value of the objective function?

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