Time left 0:58:06 PART I. PROBLEM SOLVING (10 Marks) Direction: Direction: Read, Analyze and Calculate what required. ABC manufactures a computer stand. It has fixed costs of $600,000 and each stand sells for $130, with a variable cost of $55 per unit. The factory has a maximum capacity of 25,000 units and it anticipates selling 10,000 units each period. 1- Identify the parameters of the problem (2 marks) 2- Create the mathematical model that represents the problem (2 marks) 3- If ABC manufactures sells 11,000 stands, what would be the profit? (2 marks correct solution + 1 marks correct assignment = 3 marks) 4- How much stands must XYZ manufactures sells to break even? (2 marks correct solution + 1 marks correct assignment = 3 marks) PART II. PROBLEM SOLVING (15 Marks) Direction: Direction: Read, Analyze and Calculate what required. The Reem Furniture Corporation manufactures two products, benches and picnic tables, for use in yards and parks. The firm has two main resources: its carpenters (labor force) and a supply of redwood for use in the furniture. During the next production cycle, 7,000 hours of labor are available under a union agreement. The firm also has a stock of 2,400 feet of good-quality redwood. Each bench that Outdoor Furniture produces requires 70 labor hours and 12 feet of redwood; each picnic table takes 20 labor hours and 8 feet of redwood. Completed benches will yield a profit of BD 22 each, and tables will result in a profit of BD 8 each. Formulate this problem as a linear programming problem to determine the best possible combination of benches and picnic tables to manufacture to reach the maximum profit. redwood. Each bench that Outdoor Furniture produces requires 70 Tabor hours and IZ TARTO redwood; each picnic table takes 20 labor hours and 8 feet of redwood. Completed Time left 0:59:23 yield a profit of BD 22 each, and tables will result in a profit of BD 8 each. Formulate this problem as a linear programming problem to determine the best possible combination of benches and picnic tables to manufacture to reach the maximum profit. Use: x = number of benches to be produced y = number of Picnic tables to be produced 1. Interpret the problem given above; (a) determine the objective function (2 Marks) and (b) the constraints (3 Marks). 2. Write the problem in complete form and solve using graphical method. (5 Marks) 3. Determine the value of each feasible point. (4 Marks). Find the optimal solution. (1Mark) Rubrics for marking (5 Marks) 2 Marks-Finding the x intercept points and y-intercept points for each constraint. 2 Marks- Plot the constraints using the graphical method. 1 Mark- Find the Intersection point graphically No mark shall be awarded for illogical solutions Time left 0:58:06 PART I. PROBLEM SOLVING (10 Marks) Direction: Direction: Read, Analyze and Calculate what required. ABC manufactures a computer stand. It has fixed costs of $600,000 and each stand sells for $130, with a variable cost of $55 per unit. The factory has a maximum capacity of 25,000 units and it anticipates selling 10,000 units each period. 1- Identify the parameters of the problem (2 marks) 2- Create the mathematical model that represents the problem (2 marks) 3- If ABC manufactures sells 11,000 stands, what would be the profit? (2 marks correct solution + 1 marks correct assignment = 3 marks) 4- How much stands must XYZ manufactures sells to break even? (2 marks correct solution + 1 marks correct assignment = 3 marks) PART II. PROBLEM SOLVING (15 Marks) Direction: Direction: Read, Analyze and Calculate what required. The Reem Furniture Corporation manufactures two products, benches and picnic tables, for use in yards and parks. The firm has two main resources: its carpenters (labor force) and a supply of redwood for use in the furniture. During the next production cycle, 7,000 hours of labor are available under a union agreement. The firm also has a stock of 2,400 feet of good-quality redwood. Each bench that Outdoor Furniture produces requires 70 labor hours and 12 feet of redwood; each picnic table takes 20 labor hours and 8 feet of redwood. Completed benches will yield a profit of BD 22 each, and tables will result in a profit of BD 8 each. Formulate this problem as a linear programming problem to determine the best possible combination of benches and picnic tables to manufacture to reach the maximum profit. redwood. Each bench that Outdoor Furniture produces requires 70 Tabor hours and IZ TARTO redwood; each picnic table takes 20 labor hours and 8 feet of redwood. Completed Time left 0:59:23 yield a profit of BD 22 each, and tables will result in a profit of BD 8 each. Formulate this problem as a linear programming problem to determine the best possible combination of benches and picnic tables to manufacture to reach the maximum profit. Use: x = number of benches to be produced y = number of Picnic tables to be produced 1. Interpret the problem given above; (a) determine the objective function (2 Marks) and (b) the constraints (3 Marks). 2. Write the problem in complete form and solve using graphical method. (5 Marks) 3. Determine the value of each feasible point. (4 Marks). Find the optimal solution. (1Mark) Rubrics for marking (5 Marks) 2 Marks-Finding the x intercept points and y-intercept points for each constraint. 2 Marks- Plot the constraints using the graphical method. 1 Mark- Find the Intersection point graphically No mark shall be awarded for illogical solutions
