Fountainhead Company manufactures two types of display boards that are sold to office supply stores. One board is hard-finished marking board that can be written on with a water-soluble felt-tip marking pen and then wiped clean with a cloth. The other is a conventional cork-type tack board.
Both boards pass through two manufacturing departments. All raw materials (board base, board covering, and aluminum frames) are cut to size in the Cutting Department. Both types of boards are the same size and use the same aluminum frame. The boards are assembled in either the Automated Assembly Department or the Labor Assembly Department. The Automated Department is a capital intensive assembly operation. This department has been in operation for 18 months and was intended to replace the Labor Assembly Department. However, business expanded so rapidly that both assembly operations are needed and used. The final results of the two assembly operations are identical. The only difference between the two is the proportion of machine time versus direct labor in each department and, thus, different costs. However, workers have been trained for both operations so that they can be switched between the two operations.
The company produced and sold 600,000 marking boards and 900,000 tack boards last year. Management estimates that the total unit sales volume for the coming year will increase 20% if the units can be produced. The company has contracts to produce and sell 30,000 units of each board each month. Sales, production, and cost incurrence are uniform throughout the year. The company has a monthly maximum labor capacity of 30,000 direct labor hours in the Cutting Department and 40,000 direct labor hours for the assembly operations (Automated Assembly and Labor Assembly Departments combined). It takes 12 minutes of labor in the Cutting Department for both kinds of boards. The Automated Assembly Department requires 3 minutes of labor for each board, regardless of type, and the Labor Assembly Department requires 15 minutes of labor per board.
Data regarding the two products and their manufactures follow:
QUESTION CONTINUE TO NEXT PAGE

Required:
Assuming the company wants to maximize profits, give the linear programming objective function and constraints.

Transcribed Image Text:

Board $60.00 3.00 Tack Board $45.00 3.00 Sales price per unit.. Variable marketing expenses Materials Base Covering Frame... 6.00 14.50 8.25 6.00 7.75 8.25 Direct labor Cutting Department Automated Assembly Departmentmn Labor Assembly Department 2.00 60 3.00 2.00 60 3.00 Variable factory overhead: Cutting Department.. Automated Assembly Department Labor Assembly Department.... 2.45 3.30 2.25 2.45 3.30 2.25 Machine Hour Data Automated Cutting Assembly Assembly Department Department Department Labor Machine hours required per board Monthly machine hours available.. Annual machine hours available 15 25,000 300,000 02 1,500 18,000 05 5,000 60,000