Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $67, $95, and $133, respectively. The production requirements per unit are as follows: Number of Fans Number of Cooling Coils Manufacturing Time (hours) Economy 1 1 8 Standard 1 2 12 Deluxe 1 4 14 For the coming production period, the company has 300 fan motors, 340 cooling coils, and 2000 hours of manufacturing time available. How many economy models (E), standard models (S), and deluxe models (D) should the company produce in order to maximize profit? The linear programming model for the problem is as follows: Max 67E + 95S + 133D s.t. 1E + 1S + 1D ≤ 300 Fan motors 1E + 2S + 4D ≤ 340 Cooling coils 8E + 12S + 14D ≤ 2000 Manufacturing time E, S, D ≥ 0 The computer solution is shown in the figure below. Optimal Objective Value = 17380.00000 Variable Value Reduced Cost E 180.00000 0.00000 S 0.00000 9.00000 D 40.00000 0.00000 Constraint Slack/Surplus Dual Value 1 80.00000 0.00000 2 0.00000 7.00000 3 0.00000 7.50000 Variable Objective Coefficient Allowable Increase Allowable Decrease E 67.00000 9.00000 8.10000 S 95.00000 9.00000 Infinite D 133.00000 135.00000 15.75000 Constraint RHS Value Allowable Increase Allowable Decrease 1 300.00000 Infinite 80.00000 2 340.00000 231.42860 90.00000 3 2000.00000 480.00000 810.00000 What is the optimal solution, and what is the value of the objective function? If required, round your answers to the nearest whole number. If your answer is zero, enter "0". Optimal Solution Economy models (E) 180 Standard models (S) 0 Deluxe models (D) 40 Value of the objective function $ 17380 Which constraints are binding? Fan motors: non binding Cooling coils: binding Manufacturing time: binding Which constraint shows extra capacity? How much? If constraint shows no extra capacity, enter 0 as number of units. If required, round your answers to the nearest whole number. Which constraint shows extra capacity? How much? If constraint shows no extra capacity, enter 0 as number of units. If required, round your answers to the nearest whole number. Constraints Extra capacity Number of units Fan motors yes ? Cooling coils no 0 Manufacturing time no 0
Critical Path Method
The critical path is the longest succession of tasks that has to be successfully completed to conclude a project entirely. The tasks involved in the sequence are called critical activities, as any task getting delayed will result in the whole project getting delayed. To determine the time duration of a project, the critical path has to be identified. The critical path method or CPM is used by project managers to evaluate the least amount of time required to finish each task with the least amount of delay.
Cost Analysis
The entire idea of cost of production or definition of production cost is applied corresponding or we can say that it is related to investment or money cost. Money cost or investment refers to any money expenditure which the firm or supplier or producer undertakes in purchasing or hiring factor of production or factor services.
Inventory Management
Inventory management is the process or system of handling all the goods that an organization owns. In simpler terms, inventory management deals with how a company orders, stores, and uses its goods.
Project Management
Project Management is all about management and optimum utilization of the resources in the best possible manner to develop the software as per the requirement of the client. Here the Project refers to the development of software to meet the end objective of the client by providing the required product or service within a specified Period of time and ensuring high quality. This can be done by managing all the available resources. In short, it can be defined as an application of knowledge, skills, tools, and techniques to meet the objective of the Project. It is the duty of a Project Manager to achieve the objective of the Project as per the specifications given by the client.
Quality Air Conditioning manufactures three home air conditioners: an economy model, a standard model, and a deluxe model. The profits per unit are $67, $95, and $133, respectively. The production requirements per unit are as follows:
| Number of Fans |
Number of Cooling Coils |
Manufacturing Time (hours) |
|
| Economy | 1 | 1 | 8 |
| Standard | 1 | 2 | 12 |
| Deluxe | 1 | 4 | 14 |
For the coming production period, the company has 300 fan motors, 340 cooling coils, and 2000 hours of manufacturing time available. How many economy models (E), standard models (S), and deluxe models (D) should the company produce in order to maximize profit? The linear programming model for the problem is as follows:
| Max | 67E | + | 95S | + | 133D | |||
| s.t. | ||||||||
| 1E | + | 1S | + | 1D | ≤ | 300 | Fan motors | |
| 1E | + | 2S | + | 4D | ≤ | 340 | Cooling coils | |
| 8E | + | 12S | + | 14D | ≤ | 2000 | Manufacturing time | |
| E, S, D ≥ 0 | ||||||||
The computer solution is shown in the figure below.
| Optimal Objective Value = 17380.00000 | |||||||
| Variable | Value | Reduced Cost | |||||
| E | 180.00000 | 0.00000 | |||||
| S | 0.00000 | 9.00000 | |||||
| D | 40.00000 | 0.00000 | |||||
| Constraint | Slack/Surplus | Dual Value | |||||
| 1 | 80.00000 | 0.00000 | |||||
| 2 | 0.00000 | 7.00000 | |||||
| 3 | 0.00000 | 7.50000 | |||||
| Variable | Objective Coefficient |
Allowable Increase |
Allowable Decrease |
||||||
| E | 67.00000 | 9.00000 | 8.10000 | ||||||
| S | 95.00000 | 9.00000 | Infinite | ||||||
| D | 133.00000 | 135.00000 | 15.75000 | ||||||
| Constraint | RHS Value |
Allowable Increase |
Allowable Decrease |
||||||
| 1 | 300.00000 | Infinite | 80.00000 | ||||||
| 2 | 340.00000 | 231.42860 | 90.00000 | ||||||
| 3 | 2000.00000 | 480.00000 | 810.00000 | ||||||
- What is the optimal solution, and what is the value of the objective function? If required, round your answers to the nearest whole number. If your answer is zero, enter "0".
Optimal Solution Economy models (E) 180 Standard models (S) 0 Deluxe models (D) 40 Value of the objective function $ 17380 - Which constraints are binding?
Fan motors: non bindingCooling coils: bindingManufacturing time: binding - Which constraint shows extra capacity? How much? If constraint shows no extra capacity, enter 0 as number of units. If required, round your answers to the nearest whole number.
- Which constraint shows extra capacity? How much? If constraint shows no extra capacity, enter 0 as number of units. If required, round your answers to the nearest whole number.
Constraints Extra capacity Number of units Fan motors yes? Cooling coils no0 Manufacturing time no0
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