Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here: Cabinetmaker 1 Cabinetmaker 2 Cabinetmaker 3 Hours required to complete all the oak cabinets 50 44 32 Hours required to complete all the cherry cabinets 61 46 34 Hours available 35 25 30 Cost per hour $36 $43 $56 For example, Cabinetmaker 1 estimates that it will take 50 hours to complete all the oak cabinets and 61 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 35 hours available for the final finishing operation. Thus, Cabinetmaker 1 can only complete 35/50 = 0.7, or 70%, of the oak cabinets if it worked only on oak cabinets. Similarly, Cabinetmaker 1 can only complete 35/61 = 0.57, or 57%, of the cherry cabinets if it worked only on cherry cabinets. Formulate a linear programming model that can be used to determine the proportion of the oak cabinets and the proportion of the cherry cabinets that should be given to each of the three cabinetmakers in order to minimize the total cost of completing both projects. Let O1 = proportion of Oak cabinets assigned to cabinetmaker 1 O2 = proportion of Oak cabinets assigned to cabinetmaker 2 O3 = proportion of Oak cabinets assigned to cabinetmaker 3 C1 = proportion of Cherry cabinets assigned to cabinetmaker 1 C2 = proportion of Cherry cabinets assigned to cabinetmaker 2 C3 = proportion of Cherry cabinets assigned to cabinetmaker 3 Min O1 + O2 + O3 + C1 + C2 + C3 s.t. O1 C1 ≤ Hours avail. 1 O2 + C2 ≤ Hours avail. 2 O3 + C3 ≤ Hours avail. 3 O1 + O2 + O3 = Oak C1 + C2 + C3 = Cherry O1, O2, O3, C1, C2, C3 ≥ 0 How do I define the objective function, as well as the final two constraints?
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.
Georgia Cabinets manufactures kitchen cabinets that are sold to local dealers throughout the Southeast. Because of a large backlog of orders for oak and cherry cabinets, the company decided to contract with three smaller cabinetmakers to do the final finishing operation. For the three cabinetmakers, the number of hours required to complete all the oak cabinets, the number of hours required to complete all the cherry cabinets, the number of hours available for the final finishing operation, and the cost per hour to perform the work are shown here:
| Cabinetmaker 1 | Cabinetmaker 2 | Cabinetmaker 3 | |
| Hours required to complete all the oak cabinets | 50 | 44 | 32 |
| Hours required to complete all the cherry cabinets | 61 | 46 | 34 |
| Hours available | 35 | 25 | 30 |
| Cost per hour | $36 | $43 | $56 |
For example, Cabinetmaker 1 estimates that it will take 50 hours to complete all the oak cabinets and 61 hours to complete all the cherry cabinets. However, Cabinetmaker 1 only has 35 hours available for the final finishing operation. Thus, Cabinetmaker 1 can only complete 35/50 = 0.7, or 70%, of the oak cabinets if it worked only on oak cabinets. Similarly, Cabinetmaker 1 can only complete 35/61 = 0.57, or 57%, of the cherry cabinets if it worked only on cherry cabinets.
- Formulate a linear programming model that can be used to determine the proportion of the oak cabinets and the proportion of the cherry cabinets that should be given to each of the three cabinetmakers in order to minimize the total cost of completing both projects.
Let O1 = proportion of Oak cabinets assigned to cabinetmaker 1 O2 = proportion of Oak cabinets assigned to cabinetmaker 2 O3 = proportion of Oak cabinets assigned to cabinetmaker 3 C1 = proportion of Cherry cabinets assigned to cabinetmaker 1 C2 = proportion of Cherry cabinets assigned to cabinetmaker 2 C3 = proportion of Cherry cabinets assigned to cabinetmaker 3
How do I define the objective function, as well as the final two constraints?Min O1 + O2 + O3 + C1 + C2 + C3 s.t. O1 C1 ≤ Hours avail. 1 O2 + C2 ≤ Hours avail. 2 O3 + C3 ≤ Hours avail. 3 O1 + O2 + O3 = Oak C1 + C2 + C3 = Cherry O1, O2, O3, C1, C2, C3 ≥ 0
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