ABCD Case Study
Purpose
- ABCD intends to determine the ideal number of footballs and basketballs to manufacture that will maximize the company’s net profit after taxes.
- To determine what actions the company should take in the future to increase profitability.
- To determine how much extra profit the company might expect if the action is implemented.
Problem Description
Even though ABCD has some flexibility to adjust its manufacturing effort between basketball and football production, the current manufacturing processes limit the maximum and the minimum number of each ball that the company can produce. These constraints include the production capacity, labor costs, cost of materials, and manufacturing time. Therefore, there is a need to determine the ideal number of footballs and basketballs that ABC should produce to maximize its net profits after taxes.
Methodology
The analysis used Excel Solver to carry out linear programming. The decision variables (n) denoted the ideal number of footballs and basketballs that the machine was expected to manufacture to maximize the company’s net profit after sales. The constrains covered in the model include the machine capacity in hours for both product categories, the cost of material, the maximum and the minimum number of items produced, and the cost of labor per hour.
Results
In the quest to maximize the company’s net profits after taxes, the Excel Solver output revealed that the machine should manufacture 40,000 footballs and 56,000 basketballs. This would result in a yearly revenue of $1,224,000. After applying the 28% corporate tax to the revenue, the maximum after tax profit realized by the company would be $881,280. The sensitivity analysis revealed final values for the ideal number of footballs (40,000) and basketballs (56,000), as well as the machine capacity using a Lagrange capacity of 28. The objective result for footballs was $1,224,000, with a lower limit of 40,000 and an upper limit of 60,000. For basketballs, the objective findings were $860,000 at a lower limit of 30,000 units and $1,224,000 at an upper limit of 56,000 units.
Recommendations
- ABCD should manufacture 40,000 footballs and 56,000 basketballs to maximize net profit after taxes while considering the existing constraints.
- The binding constraints are machine capacity (hours), as well as the maximum and the minimum number of units for each product category that the machine can manufacture. Therefore, ABCD should not make any changes to these constraints, as they would affect the expected output significantly.
- The company should strive to maximize the number of footballs and basketballs that it produces to increase profitability. If the company operates full capacity to produce 60,000 basketballs and 40,000 footballs, the extra profit received from the action would be $56,000.