Capacity and product mix decisions, linear programming Xu Company makes two types of wood doors: standard and deluxe. The doors are manufactured in a plant consisting of three departments: cutting, assembly, and finishing. Both labor and machine time are spent on the two products as they are worked on in each department.

In planning the production schedule for the next month, management is confronted with a labor shortage and the knowledge that some machines must be shut down for major maintenance and repair. The following information pertains to the estimated levels of capacity of direct labor hours and machine hours available next month in the three departments:

Direct labor and machine hours required per unit of each product are as follows:

The estimated demand for the next month is 13,000 units of standard doors and 5,000 units of deluxe doors. Unit cost and price information are as follows:

The average wage rate is $20 per hour and variable overhead cost is 25% times direct labor cost. Direct labor and machine availability in individual departments cannot be switched from one department to another.Required(a) Determine whether the direct labor hour and machine hour capacities are adequate to meet the next month's demand.(b) How many units of each product should the company produce to maximize its profits?(c) Suppose that as a result of process improvements, the deluxe model only requires 1.2 machine hours in finishing and 0.8 labor hour in cutting. How many units of each product should the company produce to maximize its profits?(d) Suggest other alternatives the company might consider to satisfy the estimated demand for both products.

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DEPARTMENTS CAPACITY AVAILABLE Machine hours Labor hours CUTTING FINISHING ASSEMBLY 40,000 17,500 15,000 40,000 8,000 8,000