Reference no: EM132515180

Point 1: Sheet Harbour Chemicals (SHC) manufactures chemicals manufactures chemicals used in the paint industry. The process involves three departments. Chemical A, which is purchased for $3 per liter, is processed through Department 1 in batches of 100 liters. Each batch of chemicals processed through Department A produces 70 liters of chemical B and 30 liters of chemical C.

Point 2: Chemical B is sold for $10 per liter. Chemical C is used in Departmet 2 to produce chemicals D, E, and F. Department 2 processes chemical C in batches of 200 liters. Each batch processed through Department 2 produces 100 liters of chemical D, 60 of chemical E, and 40 of chemical F.

Point 3: Chemical D is sold for $12 per liter. Chemical E is a waste product that is donated to the local municipality to be spread on gravel roads to keep down dust. Chemical F is a hazardous waste product that must be disposed of at a cost of $6 per liter. Alternatively, chemical F can be processed through Department 3 to produce chemical C.

Point 4: Department 3 processes chemical F in batches of 40 liters. For each batch of chemical F processed, 20 liters of chemical C are produced. In the past, this operation has had a tendency to build up stocks of chemical C. The maximum storage has had a tendency to build up stocks of chemical C. The maximum storage capacity for Chemical C is 1,000 liters.

Point 4: The sales manager indicates that sales of chemical B cannot excess 35,000 liters in the upcoming period, and sales of chemical D cannot exceed 10,000 liters. The production manager advises that 7,000 labor-hours are available for the upcoming period. Workers are paid $10 per hour worked. The production manager indicates that the labor-hours required for each batch in departments 1, 2, and 3 are 10, 15, and 10, respectively. Moreover, because of constraints relating to the mixing vats and storage, the max number of batches in Departments 1, 2, and 3 are 600, 80, and 40, respectively. The estimate variable overhead costs per batch in departments 1, 2, and 3 are estimated as $250, $750, and $100.

Question 1: What are the decision variables?

Question 2: What is the objective function?

Question 3: What contributes to the objective function?

Question 4: What are the constraints?

Question 5: Find the optimal production plan.