Fisher Company produces two types of components for airplanes: A and B, with unit contribution margins of $400 and $600, respectively. The components pass through three sequential processes: cutting, welding, and assembly. Data pertaining to these processes and market demand are given below (weekly data). Resource Resource Available Resource Usage (A) Resource Usage (B) Cutting 300 machine hours Six hours Ten hours Welding 308 welding hours Ten hours Six hours Assembly 400 labor hours Four hours Ten hours Market demand (A) 50 One unit Zero units Market demand (B) 40 Zero units One unit Required: 1. Express Fisher Company's constrained optimization problem as a linear programming model. If an an answer box does not require an entry, enter "0" for your answer. Objective function: Max Z = $400 A + $600 B Internal constraints: 6A + 10 B ≤ 300 (cutting) 10A + 6B ≤ 308 (welding) 4A + 10B ≤ 400 (assembly) External constraints: A ≤ 50 B ≤ 40 Nonnegativity constraints: A ≥ 0 B ≥ 0 3. What if Fisher Company had 10 additional machine hours (cutting) with all other resources held constant? What is the new optimal mix? Enter the appropriate corner point for your answer. Answer: F What is the associated total contribution margin? Round the units of A and B to two decimal places, and round intermediate calculations and your final answer to the nearest dollar. What is the incremental benefit per machine hour caused by the additional ten hours, if any?
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.
Constrained Optimization: Multiple Internal Constraints
Fisher Company produces two types of components for airplanes: A and B, with unit contribution margins of $400 and $600, respectively. The components pass through three sequential processes: cutting, welding, and assembly. Data pertaining to these processes and market demand are given below (weekly data).
| Resource | Resource Available | Resource Usage (A) | Resource Usage (B) |
| Cutting | 300 machine hours | Six hours | Ten hours |
| Welding | 308 welding hours | Ten hours | Six hours |
| Assembly | 400 labor hours | Four hours | Ten hours |
| Market demand (A) | 50 | One unit | Zero units |
| Market demand (B) | 40 | Zero units | One unit |
Required:
1. Express Fisher Company's constrained optimization problem as a linear programming model. If an an answer box does not require an entry, enter "0" for your answer.
Objective function: Max Z = $400 A + $600 B
| Internal constraints: | 6A + 10 B ≤ 300 | (cutting) |
| 10A + 6B ≤ 308 | (welding) | |
| 4A + 10B ≤ 400 | (assembly) | |
| External constraints: | A ≤ 50 | |
| B ≤ 40 | ||
| Nonnegativity constraints: | A ≥ 0 | |
| B ≥ 0 |
3. What if Fisher Company had 10 additional machine hours (cutting) with all other resources held constant? What is the new optimal mix? Enter the appropriate corner point for your answer.
Answer: F
What is the associated total contribution margin? Round the units of A and B to two decimal places, and round intermediate calculations and your final answer to the nearest dollar.
What is the incremental benefit per machine hour caused by the additional ten hours, if any?
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