Constrained Optimization: One Internal Binding Constraint Patz Company produces two types of machine parts: Part A and Part B, with unit contribution margins of $100 and $200, respectively. Assume initially that Patz can sell all that is produced of either component. Part A requires two hours of assembly, and B requires five hours of assembly. The firm has 100 assembly hours per week. Required: 1. Express the objective of maximizing the total contribution margin subject to the assembly-hour constraint. Objective function: Max Z = $100 A + $200 B Subject to: fill in the blank 1 A + fill in the blank 2 B ≤ fill in the blank 3 2. Identify the optimal amount that should be produced of each machine part. If none of the components should be produced, enter "0" for your answer. Component A fill in the blank 4 units Component B fill in the blank 5 units Identify the total contribution margin associated with this mix. $fill in the blank 6 3. What if market conditions are such that Patz can sell at most 25 units of Part A and 20 units of Part B? Express the objective function with its associated constraints for this case. Objective function: Max Z = $100 A + $200 B Assembly-hour constraint fill in the blank 7 A + fill in the blank 8 B ≤ fill in the blank 9 Demand constraint for Part A A ≤ fill in the blank 10 Demand constraint for Part B B ≤ fill in the blank 11 Identify the optimal mix and its associated total contribution margin. Component A $fill in the blank 12 units Component B $fill in the blank 13 units Total contribution $fill in the blank 14
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: One Internal Binding Constraint
Patz Company produces two types of machine parts: Part A and Part B, with unit contribution margins of $100 and $200, respectively. Assume initially that Patz can sell all that is produced of either component. Part A requires two hours of assembly, and B requires five hours of assembly. The firm has 100 assembly hours per week.
Required:
1. Express the objective of maximizing the total contribution margin subject to the assembly-hour constraint.
Objective function: Max Z = $100 A + $200 B
Subject to: fill in the blank 1 A + fill in the blank 2 B ≤ fill in the blank 3
2. Identify the optimal amount that should be produced of each machine part. If none of the components should be produced, enter "0" for your answer.
| Component A | fill in the blank 4 | units |
| Component B | fill in the blank 5 | units |
Identify the total contribution margin associated with this mix.
$fill in the blank 6
3. What if market conditions are such that Patz can sell at most 25 units of Part A and 20 units of Part B? Express the objective function with its associated constraints for this case.
Objective function: Max Z = $100 A + $200 B
| Assembly-hour constraint | fill in the blank 7 A + fill in the blank 8 B ≤ fill in the blank 9 |
| Demand constraint for Part A | A ≤ fill in the blank 10 |
| Demand constraint for Part B | B ≤ fill in the blank 11 |
Identify the optimal mix and its associated total contribution margin.
Component A $fill in the blank 12 units
Component B $fill in the blank 13 units
Total contribution $fill in the blank 14
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
