# LINEAR PROGRAMMING PROBLEMS Case Solution & Answer

## Linear Programming Problems Case Solution

### P6

• The new requirement is the 20 percent discount if the iron sales increased from 600 units per month for each item. This increase in requirements will decrease the price of the item if the sales will increase 600 units per month for each item which will change the slope of the line. A change in slope will result in the movement of the line which will not meeting the linearity requirements. A change in slope will directly affect the linear line which will shift the model from linear to non-linear programming.
• The new contribution coefficients have been calculated by using the IF function. The IF function says if that if the company’s iron sales will exceed the 600 units, then the company will reduce the retail price by 20 percent.
• The average net profit for each iron set is calculated by assuming that the initial production unit is only 1. Theaverage net profit for each iron set is mentioned in below table.
 Iron Set Contribution Coefficients C Forged Irons 315.11 Clean Pro Irons 403.7533333 Clean Shot Irons 470.255 Hybrid Set 862.13 Hybrids/Irons Combo Set 875.6483333 Pro Irons 789.605 Pro Irons/Hybrids Combo Set 989.4166667 Prototype Irons 484.62 Standard Irons 211.6266667 X Forged Irons 236.5816667
• The below mentioned table is showing the total profits which have been generated by using the excel solver. The detail function is located in excel sheet.
 Iron Set Average of Raw Materials Cost Actual Retail Contribution Coefficients Actual Demand Average Net Profits Total Profit Total Used Machine Hours C Forged Irons \$        264.75 \$         699.99 315.11 532 \$            167,639 \$        3,216,922 15944 Clean Pro Irons \$        184.84 \$         699.99 403.75 541 \$            218,431 Clean Shot Irons \$        219.47 \$         799.99 470.26 548 \$            257,700 Hybrid Set \$        221.33 \$      1,199.99 862.13 587 \$            506,070 Hybrids/Irons Combo Set \$        211.14 \$      1,199.99 875.65 589 \$            515,757 Pro Irons \$        198.12 \$      1,099.99 789.61 579 \$            457,181 Pro Irons/Hybrids Combo Set \$        190.84 \$      1,299.99 989.42 600 \$            593,650 Prototype Irons \$        202.17 \$         799.99 484.62 549 \$            266,056 Standard Irons \$        173.76 \$         499.99 211.63 522 \$            110,469 X Forged Irons \$        250.34 \$         599.99 236.58 524 \$            123,969
• By using the answer report, it has been identified that the results are less sensitive because if the company wants to produce more units, the have all resources available because the 0 value in slack variable have not been found.

### P6

• The problem has been formulated in the excel workbook in which thee decision variables are the manufacturing of the running, hiking and casual shoes. In addition to this all of the limitations have been added as a constraint in the model which are at least manufacturing of 100 units of each model, the maximum production of casual and running shoes up to the 300 units and the limitations related to the machine hours for each department.
• The deviational variables are running shoes and casual shoes because the demand of the running shoes and casual shoes are 300 pair of shoes while the demand of hiking shoes are unknown, so, the deviational variables are casual and running pair of shoes.
• The system constraints are the shoe model which are at least manufacturing of 100 units of each model, the maximum production of casual and running shoes up to the 300 units and the limitations related to the machine hours for each department such as the maximum production hours for cutting department are 1000, for finishing department are 600 and for packaging department are 500. In addition to this, an additional limitation has been put in the model which is that the hiking shoe production, casual shoe production and running shoe production must be an integer.
• The model has been formulated in the excel workbook.
• The solver provides the following results
 Products Profit per item Cutting hour Finishing hour Packaging hour Demand Minimum Production Running 30 2 0.5 1.5 300 100 Hiking 40 3 1.5 0.125 100 Casual 20 1 0.5 1.5 300 100

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