Problem 2: Silica Chemicals (Production Planning with Multiple Resource Constraints) Silica Chemicals produces two fertilizers, SC1 and SC2, at its Lafayette plant. This plant operates 40 hours per week and employs five full-time workers as well as two part-time workers to run their seven blending machines that mix certain chemicals to produce each fertilizer. This work force can provide up to 230 hours of labor in the Blending Department. The products, once blended, are packaged in the Bagging Department, which currently has seven bagging machines and employs six full-time workers and one part-time worker. This work force can provide up to 250 hours of labor in the Bagging Department. The hours required in the Blending and Bagging Departments to produce one thousand pounds of each of the fertilizers are listed in the table below: SCI 2 1 Blending Bagging - SC2 1 2 The company's cost manager estimates a contribution margin of $400 per thousand pounds of SC1 and $600 per thousand pounds of SC2. The company has unlimited access to raw materials (i.e. raw materials is not a constraint). Demand for SC2, which is a specialized product, is limited to 120,000 pounds per week. a) Determine the optimal product mix. (3 points) b) Say, the plant's production head lays off all part-time workers in the Blending department reducing the available labor hours in Blending from 230 to 200. By how much will the company's total contribution change because of this action? (1 point) c) Say, the plant's production head converts the part-time worker in the Bagging department into a full-time worker thereby increasing the available labor hours in Bagging by 30. By how much will the company's total contribution change because of this action? (1 point) Problem 2: Silica Chemicals (Production Planning with Multiple Resource Constraints) Silica Chemicals produces two fertilizers, SC1 and SC2, at its Lafayette plant. This plant operates 40 hours per week and employs five full-time workers as well as two part-time workers to run their seven blending machines that mix certain chemicals to produce each fertilizer. This work force can provide up to 230 hours of labor in the Blending Department. The products, once blended, are packaged in the Bagging Department, which currently has seven bagging machines and employs six full-time workers and one part-time worker. This work force can provide up to 250 hours of labor in the Bagging Department. The hours required in the Blending and Bagging Departments to produce one thousand pounds of each of the fertilizers are listed in the table below: SCI 2 1 Blending Bagging - SC2 1 2 The company's cost manager estimates a contribution margin of $400 per thousand pounds of SC1 and $600 per thousand pounds of SC2. The company has unlimited access to raw materials (i.e. raw materials is not a constraint). Demand for SC2, which is a specialized product, is limited to 120,000 pounds per week. a) Determine the optimal product mix. (3 points) b) Say, the plant's production head lays off all part-time workers in the Blending department reducing the available labor hours in Blending from 230 to 200. By how much will the company's total contribution change because of this action? (1 point) c) Say, the plant's production head converts the part-time worker in the Bagging department into a full-time worker thereby increasing the available labor hours in Bagging by 30. By how much will the company's total contribution change because of this action? (1 point)
