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Problem #1: A workshop has three (3) types of machines A, B and C; it can manufacture two (2) products 1 and 2, and all products have to go to each machine and each one goes in the same order; First to the machine A, then to B and then to C. The following table shows: The hours needed at each machine, per product unit the total available hours for each machine, per week; and the profit of each product per unit sold Type of Machine Available Hours/Week 16 12 28 Product 1 Product 2 B 1 4 Profit Per Unit $1 $1.50 Required: Formulate and solve using the graphical method a Linear Programming model for the information above. Make certain you 1. Be certain to draw in ALL constraints, 2. Indicate the area above or below the line that represents the solutions to that equation (use arrows off of the line), 3. Identify the area where all constraints are satisfied and label it, 4. Identify all vertices on the graph and test ALL vertices as possible optimal solutions, 5. Compute the objective function value for every vertex and identify the optimal solution. 6. State the optimal solution combination to be produced and the profit to be expected. 7. Confirm your answers using SOLVER. Decision Variables: X: Product 1 Units to be produced weekly • Y: Product 2 Units to be produced weekly

Problem #1: A workshop has three (3) types of machines A, B and C; it can manufacture two (2) products 1 and 2, and all products have to go to each machine and each one goes in the same order; First to the machine A, then to B and then to C. The following table shows: The hours needed at each machine, per product unit the total available hours for each machine, per week; and the profit of each product per unit sold Type of Machine Available Hours/Week 16 12 28 Product 1 Product 2 B 1 4 Profit Per Unit $1 $1.50 Required: Formulate and solve using the graphical method a Linear Programming model for the information above. Make certain you 1. Be certain to draw in ALL constraints, 2. Indicate the area above or below the line that represents the solutions to that equation (use arrows off of the line), 3. Identify the area where all constraints are satisfied and label it, 4. Identify all vertices on the graph and test ALL vertices as possible optimal solutions, 5. Compute the objective function value for every vertex and identify the optimal solution. 6. State the optimal solution combination to be produced and the profit to be expected. 7. Confirm your answers using SOLVER. Decision Variables: X: Product 1 Units to be produced weekly • Y: Product 2 Units to be produced weekly

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
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: A workshop has three (3) types of machines A, B, and C; it can manufacture two (2) products 1 and 2, and all products have to go to each machine and each one goes in the same order; First to the machine A, then to B and then to C.

The following table shows The hours needed at each machine, per product unit the total available hours for each machine, per week; and the profit of each product per unit sold

Problem #1: A workshop has three (3) types of machines A, B and C; it can manufacture two (2) products 1 and 2, and all products have to go to each machine and each one goes in the same order; First to the machine A, then to B and then to C. The following table shows: The hours needed at each machine, per product unit the total available hours for each machine, per week; and the profit of each product per unit sold Type of Machine Product 1 Product 2 Available Hours/Week A 2 16 B 1 12 C 4 2 28 Profit Per Unit S1 $1.50 Required: Formulate and solve using the graphical method a Linear Programming model for the information above. Make certain you 1. Be certain to draw in ALL constraints, 2. Indicate the area above or below the line that represents the solutions to that equation (use arrows off of the line), 3. Identify the area where all constraints are satisfied and label it, 4. Identify all vertices on the graph and test ALL vertices as possible optimal solutions, 5. Compute the objective function value for every vertex and identify the optimal solution. 6. State the optimal solution combination to be produced and the profit to be expected. 7. Confirm your answers using SOLVER. Decision Variables: X: Product 1 Units to be produced weekly • Y: Product 2 Units to be produced weekly
Transcribed Image Text:Problem #1: A workshop has three (3) types of machines A, B and C; it can manufacture two (2) products 1 and 2, and all products have to go to each machine and each one goes in the same order; First to the machine A, then to B and then to C. The following table shows: The hours needed at each machine, per product unit the total available hours for each machine, per week; and the profit of each product per unit sold Type of Machine Product 1 Product 2 Available Hours/Week A 2 16 B 1 12 C 4 2 28 Profit Per Unit S1 $1.50 Required: Formulate and solve using the graphical method a Linear Programming model for the information above. Make certain you 1. Be certain to draw in ALL constraints, 2. Indicate the area above or below the line that represents the solutions to that equation (use arrows off of the line), 3. Identify the area where all constraints are satisfied and label it, 4. Identify all vertices on the graph and test ALL vertices as possible optimal solutions, 5. Compute the objective function value for every vertex and identify the optimal solution. 6. State the optimal solution combination to be produced and the profit to be expected. 7. Confirm your answers using SOLVER. Decision Variables: X: Product 1 Units to be produced weekly • Y: Product 2 Units to be produced weekly
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