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.

Required:
1. Calculate the monthly requirement for machine hours and direct labor hours for producing Products 401, 402, and 403 to determine whether or not the factory can meet the monthly sales demand.
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.
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. Prepare a schedule that shows the contribution to profits from this optimal mix. (CMA adapted)LO1

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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 Product Unit Produced 401 Labor hours 2 Machine hours 1 402 Labor hours Machine hours 1 403 Labor hours 2 Machine hours 2 312122 3221 Calen believes that the monthly demand for the next six months will be as follows: Product 401 Units Sold 402 403 500 400 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: