At a chip manufacturing plant, four technicians (A, B, C, and D) produce three products (Products 1, 2, and 3). This month, the chip manufacturer can sell 80 units of Product 1, 50 units of Product 2, and, at most, 50 units of Product 3. Technician A can make only Products 1 and 3. Technician B can make only Products 1 and 2. Technician C can make only Product 3. Technician D can make only Product 2. For each unit produced, the products contribute the following profit: Product 1, $6; Product 2, $7; and Product 3, $10. The time (in hours) each technician needs to manufacture a product is as follows: productTech ATech BTech CTech D
12 hrs2.5 hrscannot docannot do
2cannot do3 hrscannot do3.5 hrs
33 hrscannot do4 hrscannot do
Each technician can work up to 120 hours per month. How can the chip manufacturer maximize its monthly profit? Assume a fractional number of units can be produced.
Deliverables:
1. A complete algebraic formulation of the linear programming model. This should include a description of the decision variables and an explanation of the objective function and constraints.
2. Computer output of your solution and ranging from POM-QM.
3. A report (MS-Word document) to management describing your objective and production plan. Many young professionals believe that they will be evaluated entirely on whether the numbers are right and this is simply not true. Managers are busy people who have little time or patience to wade through poorly written reports.