Page 199, Problem 4Solution by Mr. Imad FeghaliSolve problem 4 on page 199 using WinQSB. Change the order of the goals and create a table similar to the Table 56 on page 197. Write a report for a manager and explain the resultsof this table. Product Labor (hours) Profit MarketingX1 4 $4 Min 7 unitsX2 2 $2 Min 10 units Max = 32 hours Goal $48 4 X1 + 2 X2 <= 324 X1 + 2 X2 >= 48X1 >= 7X2 >= 10We will use the proposed penalty cost defined in the problem and try to solveit based on available penalty costs and Goal Programming. We define theconstraints as follows:4 X1 + 2 X2 + S1N – S1P = 324 X1 + 2 X2 + S2N – S2P = 48X1 + S3N – S3P = 7X2 + S4N – S4P = 10As it is clear SiP and SiN are the deviational variables. Now we can define ourobjective function as one which minimizes the penalty for the company. O.F. Min Z= 2 S1P + 1 S1N + 1 S2N + 5 S3N + 5 S4NTable 1: WinQSB input data spreadsheetIMAD FEGHALI ADVANCED METHODS IN OR / SPRING 2005Table 2: WinQSB output data spreadsheetNow in order to use preemptive goal programming and without having thedefined penalty cost, just by priority explained in the problem we have thefollowing goals and priorities with the same constraints to achieve:OF:Z1=P1 S1NZ2=P2 S3NZ3= P3 S4NZ4= P4 S1P2IMAD FEGHALI ADVANCED METHODS IN OR / SPRING 2005ST:4 X1 + 2 X2 + S1N – S1P = 324 X1 + 2 X2 + S2N – S2P = 48 not required just greater than signX1 + S3N – S3P = 7X2 + S4N – S4P = 10Table 3: WinQSB input data spreadsheetTable 4: WinQSB output data spreadsheet3IMAD FEGHALI ADVANCED METHODS IN OR / SPRING 2005 Table 5. Sensitivity AnalysisHighest 2nd High 3rd High Lowest Z1 Z2 Z3 Z4S1N S3N S4N S1P 0 0 0 16S1N S3N S1P S4N 0 0 0 8S1N S4N S3N S1P 0 0 0 16S1N S4N S1P S3N 0 0 0 4S1N S1P S3N S4N 0 0 0 8S1N S1P S4N S3N 0 0 0 4S3N S1N S4N S1P 0 0 0 16S3N S1N S1P S4N 0 0 0 8S3N S4N S1P S1N 0 0 16 0S3N S4N S1N S1P 0 0 0 16S3N S1P S1N S4N 0 0 0 8S3N S1P S4N S1N 0 0 8 0S4N S1N S3N S1P 0 0 0 16S4N S1N S1P S3N 0 0 0 4S4N S3N S1N S1P 0 0 0 16S4N S3N S1P S1N 0 0 16 0S4N S1P S1N S3N 0 0 0 4S4N S1P S3N S1N 0 0 4 0S1P S1N S3N S4N 0 0 0 8S1P S1N S4N S3N 0 0 0 4S1P S3N S4N S1N 0 0 8 0S1P S3N S1N S4N 0 0 0 8S1P S4N S1N S3N 0 0 0 4S1P S4N S3N S1N 0 0 4 0Report to ManagerBased on the ranking of goals we received, the optimal solution is to produce 7units of product 1 and 10 units of product 2. This solution means that our client willspend 16 additional hours than what he desires (32 hours) to complete this task, but inthe same time will meet the requirements of not spending less hours than whatavailable, and produce exactly 7 units of Product 1 and 10 units of Product 2 asdesired.If the client did not have a ranking for the goals, which means that all goals are equal in terms of importance, the optimal solution in this case would be to produce 7 units of Product 1 and 10 units of Product 2. This solution will leave the client with 16 additional spent hours or a penalty of $32.In addition, a sensitivity analysis was performed on ranking of the goals and resultswere presented in the table above. This table would help the client see how resultschange depending on the ranking of his four goals. This gives our client a clearvision on how it can manage its losses or penalty in relation to its priority