Question

matlab code

Task 3 (36 points +4 points for commenting): Write computer code that performs the Simplex Method of Linear Programming to determine the optimal solution of the following problem statement. A manufacturer makes three types of plastic fixtures. The time in hours required for molding, trimming, and packaging of each fixture is given in the table below. Type Z 1.5 Type X Type Y Total Time Available Process Molding Trimming Packaging Profit per Fixture $11 12000 4600 2400 2/3 0.5 2/3 1/3 $16 0.5 $15 For this task, you are allowed to set the problem up by hand if you choose, and then enter the initial tableu into the code. Your code should then work through the Simplex method to find the optimal solution. Alternatively, if you would like to have your code start from the table above as the input, that would be even better. a) How many of each type of plastic fixture should be produced to maximize profit? b) What is the maximum profit?

Answer 1

Decision Variables Number of units of each type to be produced Type X Type Y 4 No.of units Objective function Maximize total profit 7 -B4*11+C4*16+D4 15 Constraints 10 (2/3)*B4+(2/3)*C4+D4 11 0.5*B4+(1/3)*C4+0.5*D4 12 12000 4600 2400

1 Decision Variables 2 Number of units of each type to be produced Type X Type Y Type Z 4 No.of units 5 Objective function Maximize total profit 0 Constraints C) C) 0 12000 10 2400 12

Solver Parameters SAS7 Set Objective To: ⓔMax OMin。Value Of: By Changing Variable Cells: Subject to the Constraints: SAS9:SAS11SCS9:SCS11 Add Change Delete Reset All Load/Save Make Unconstrained Variables Non-Negative Select a Solving Method: Simplex LP Options Solving Method Select the GRG Nonlinear engine for Solver Problems that are smooth nonlinear. Select the LP Simplex engine for linear Solver Problems, and select the Evolutionary engine for Solver problems that are non-smooth. Help Solve Close

1 Decision Variables 2 Number of units of each type to be produced TypeXType Y 4 No.of units 600 5100 800 5 Objective function 7 100200 9 12000 Maximize total profit Constraints 10 4600 4600 2400 2400 12 13