Prepare a schedule that shows the contribution to profits from this optimal mix. (CMA adapted) Calen Company Contribution to Profits from Optimal Sales Mix Product Contribution to Profits Product 401 250 Product 402 400 Product 403 1,000 Total contribution to profits 1,650 Product Mix Decisions Calen Company manufactures and sells three products in a factory of three departments. Both labor and machine time are applied to the products as they pass through each department. The nature of the machine processing and of the labor skills required in each department is such that neither machines nor labor can be switched from one department to another. Calen's management is attempting to plan its production schedule for the next several months. The planning is complicated by the fact that labor shortages exist in the community and some machines will be down several months for repairs. Following is information regarding available machine and labor time by department and the machine hours and direct labor hours required per unit of product. These data should be valid for at least the next six months. Department Monthly Capacity 1 2 3 Labor hours available 3,700 4,500 2,750 Machine hours available 3,000 3,100 2,700 Input per Unit Product Produced 1 2 3 401 Labor hours 2 3 3 Machine hours 1 1 2 402 Labor hours 1 2 Machine hours 1 1 403 Labor hours 2 2 2 Machine hours 2 2 1 Calen believes that the monthly demand for the next six months will be as follows: Product Units Sold 401 500 402 400 403 1,000 Inventory levels will not be increased or decreased during the next six months. The unit cost and price data for each product are as follows: Product 401 402 403 Unit costs: : Direct material $7 $13 $17 Direct labor 66 38 51 Variable overhead 27 20 25 Fixed overhead 15 10 32 Variable selling 3 2 4 4 Total unit cost $118 $83 $129 Unit selling price $196 $123 $167 Required: 1. Calculate the monthly requirement for machine hours and direct labor hours for producing Products 401, 402, and 403. Labor hours Machine hours Product 401 4,000 2,000 Product 402 1,200 800 Product 403 6,000 5,000 Total 11,200 7,800 Which departments can meet the monthly sales demand? All departments except for department 3 2. Determine the quantities of 401, 402, and 403 that should be produced monthly to maximize profits. Prepare a schedule that shows the contribution to profits of your product mix. Calen Company Product Mix and Contribution Margin Number of Units Contribution to profits Product Product 401 250 93 Product 402 400 50 Product 403 1,000 70 Total contribution margin 113,230 3. Assume that the machine hours available in Department 3 are 1,500 instead of 2,700. Calculate the optimal monthly product mix using the graphing approach to linear programming. 1,000 7 1.400 1,200 - E 1.000 800 000 400 200 B 0 A 0 100 200 300 400 500 600 700 800 900 1.000 Corner Point Optimal Monthly Product Mix A $ 20,000 B $ 66,500 $ 101,500 D $ 113,250 E $ 90,000 Prepare a schedule that shows the contribution to profits from this optimal mix. (CMA adapted) Calen Company Contribution to Profits from Optimal Sales Mix Product Contribution to Profits Product 401 250 Product 402 400 Product 403 1,000 Total contribution to profits 1,650 Product Mix Decisions Calen Company manufactures and sells three products in a factory of three departments. Both labor and machine time are applied to the products as they pass through each department. The nature of the machine processing and of the labor skills required in each department is such that neither machines nor labor can be switched from one department to another. Calen's management is attempting to plan its production schedule for the next several months. The planning is complicated by the fact that labor shortages exist in the community and some machines will be down several months for repairs. Following is information regarding available machine and labor time by department and the machine hours and direct labor hours required per unit of product. These data should be valid for at least the next six months. Department Monthly Capacity 1 2 3 Labor hours available 3,700 4,500 2,750 Machine hours available 3,000 3,100 2,700 Input per Unit Product Produced 1 2 3 401 Labor hours 2 3 3 Machine hours 1 1 2 402 Labor hours 1 2 Machine hours 1 1 403 Labor hours 2 2 2 Machine hours 2 2 1 Calen believes that the monthly demand for the next six months will be as follows: Product Units Sold 401 500 402 400 403 1,000 Inventory levels will not be increased or decreased during the next six months. The unit cost and price data for each product are as follows: Product 401 402 403 Unit costs: : Direct material $7 $13 $17 Direct labor 66 38 51 Variable overhead 27 20 25 Fixed overhead 15 10 32 Variable selling 3 2 4 4 Total unit cost $118 $83 $129 Unit selling price $196 $123 $167 Required: 1. Calculate the monthly requirement for machine hours and direct labor hours for producing Products 401, 402, and 403. Labor hours Machine hours Product 401 4,000 2,000 Product 402 1,200 800 Product 403 6,000 5,000 Total 11,200 7,800 Which departments can meet the monthly sales demand? All departments except for department 3 2. Determine the quantities of 401, 402, and 403 that should be produced monthly to maximize profits. Prepare a schedule that shows the contribution to profits of your product mix. Calen Company Product Mix and Contribution Margin Number of Units Contribution to profits Product Product 401 250 93 Product 402 400 50 Product 403 1,000 70 Total contribution margin 113,230 3. Assume that the machine hours available in Department 3 are 1,500 instead of 2,700. Calculate the optimal monthly product mix using the graphing approach to linear programming. 1,000 7 1.400 1,200 - E 1.000 800 000 400 200 B 0 A 0 100 200 300 400 500 600 700 800 900 1.000 Corner Point Optimal Monthly Product Mix A $ 20,000 B $ 66,500 $ 101,500 D $ 113,250 E $ 90,000