Problem 1, see picturePlease information for C is different from the one solution found online: 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 canmanufacture two (2) products 1 and 2, and all products have to go to each machineand 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 unitthe total available hours for each machine, per week; and the profit of each product perunit soldType of MachineProduct 1Product 2Available Hours/WeekA216B112C4228Profit Per UnitS1$1.50Required: Formulate and solve using the graphical method a Linear Programming modelfor the information above. Make certain you1. Be certain to draw in ALL constraints,2. Indicate the area above or below the line that represents the solutions to thatequation (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 optimalsolutions,5. Compute the objective function value for every vertex and identify the optimalsolution.6. State the optimal solution combination to be produced and the profit to beexpected.7. Confirm your answers using SOLVER.Decision Variables:X: Product 1 Units to be produced weekly• Y: Product 2 Units to be produced weekly

Max Z = X+1.5Y Constraints: 1. Machine A: 2X+2Y≤16 2. Machine B: X+2Y≤12 3. Machine C: 4X+2Y≤28

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

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter5: Network Models

Section5.3: Assignment Models

Problem 10P