please help

Subject: Operations Research 2

Topic: Goal Programming

A gament factory produces children's dress (D) and boy's shirts (S) daily. The demand of children's dress and boy' shirts for next 5 months is at least 200 each, respectively. The table below shows the processing time and the maximum time availability of each process for the next The partern-making and finishing process as at most 300 hours. The production of these products will generate a profit of PhP150,000. In order to determine the number of products that will be produced, the owner of the garment factory has set the following goals which are all equally weighted: Goal 1: Minimize the finishing processing time. Goal 2: The minimum processing time in sewing department should be at least 200 hours. Goal 3: The cutting processing time should be at most 300 hours. Furthermore, management gives a penalty of 5 for not achieving goal 2 and a penalty of 2 for overachieving goal 3 . 1) Formulate the problem as a GP Model. Use the variable indicated in the table as the decision variable for each product. (20 points) 2) a) Graph the systems constraints and label completely. (10 points) b) Determine the feasible region. ( 5 points) 3) a) Graph the Goal 1 constraint and label completely. (5 points) b) Determine the possible solutions of Goal 1 and determine the values of the deviational variables for each possible solution. (10 points) 4) a) Graph Goal 2 constraint and label completely. (5 points) b) Determine the possible solutions of Goal 2 and determine the values of the deviational variables for each possible solution. (10 points) A gament factory produces children's dress (D) and boy's shirts (S) daily. The demand of children's dress and boy' shirts for next 5 months is at least 200 each, respectively. The table below shows the processing time and the maximum time availability of each process for the next The partern-making and finishing process as at most 300 hours. The production of these products will generate a profit of PhP150,000. In order to determine the number of products that will be produced, the owner of the garment factory has set the following goals which are all equally weighted: Goal 1: Minimize the finishing processing time. Goal 2: The minimum processing time in sewing department should be at least 200 hours. Goal 3: The cutting processing time should be at most 300 hours. Furthermore, management gives a penalty of 5 for not achieving goal 2 and a penalty of 2 for overachieving goal 3 . 1) Formulate the problem as a GP Model. Use the variable indicated in the table as the decision variable for each product. (20 points) 2) a) Graph the systems constraints and label completely. (10 points) b) Determine the feasible region. ( 5 points) 3) a) Graph the Goal 1 constraint and label completely. (5 points) b) Determine the possible solutions of Goal 1 and determine the values of the deviational variables for each possible solution. (10 points) 4) a) Graph Goal 2 constraint and label completely. (5 points) b) Determine the possible solutions of Goal 2 and determine the values of the deviational variables for each possible solution. (10 points) 5) a) Graph Goal 3 constraint and label completely. (5 points) b) Determine the possible solutions of Goal 3 and determine the values of the deviational variables for each possible solution. (10 points) 6) Determine the satisficing solutions by indicating the values of the decision variables and the Z value. (10 points) 7) Determine whether the goals are achieved or not. If not achieved determine whether it is underachieved or overachieved and by what amount? ( 10 points)