Question

The SkyLight Company produces two light fixtures (products 1 and 2) that require both metal frame parts and electrical components. Management wants to determine how many units of each product to produce so as to maximize profit. For each unit of product 1, two unit of frame parts and two units of electrical components are required. For each unit of product 2, three units of frame parts and two unit of electrical components are required. The company has 240 units of frame parts and 200 units of electrical components. Each unit of product 1 gives a profit of $1, and each unit of product 2 gives a profit of $3. No more than 60 units of product 2 should be produced.

1. Formulate this linear programming model algebraically.
2. Use the graphical method (by drawing the objective function line) to solve this model, determine the optimal solution and maximum profit.
3. Write down the coordinate of all corner points.
4. How does the optimal solution change if the maximum unit of product 2 is increased to 80 units? Use the graphical method to solve the new model.
5. Formulate the model in (a) using Excel spreadsheet. Identify the data cells, the changing cells, and the objective cell.
6. Solve the model using Excel Solver. Write down the optimal solution, and value of slack variables of each constraint.

Answer 1