Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and C. The labor-hour requirements, by department, are as follows. Department Product 1 Product 2 Product 3 A 1.50 3.00 2.00 B 2.00 1.00 2.50 C 0.25 0.25 0.25 During the next production period, the labor-hours available are 450 in department A, 350 in department B, and 50 in department C. The profit contributions per unit are $26 for product 1, $27 for product 2, and $31 for product 3. (a) Formulate a linear programming model for maximizing total profit contribution. (Let Pi = units of product i produced, for i = 1, 2, 3.) Max s.t.Department A Department B Department C P1, P2, P3 ≥ 0 (b) Solve the linear program formulated in part (a). How much of each product should be produced, and what is the projected total profit contribution (in dollars)? (P1, P2, P3) = with profit $ . (c) After evaluating the solution obtained in part (b), one of the production supervisors noted that production setup costs had not been taken into account. She noted that setup costs are $400 for product 1, $520 for product 2, and $650 for product 3. If the solution developed in part (b) is to be used, what is the total profit contribution (in dollars) after taking into account the setup costs? $ (d) Management realized that the optimal product mix, taking setup costs into account, might be different from the one recommended in part (b). Formulate a mixed-integer linear program that takes setup costs into account. Management also stated that we should not consider making more than 145 units of product 1, 150 units of product 2, or 175 units of product 3. (Let Pi = units of product i produced and yi be the 0-1 variable that is one if any quantity of product i is produced and zero otherwise, for i = 1, 2, 3.) What is the objective function of the mixed-integer linear program? Max In addition to the constraints from part (a), what other constraints should be added to the mixed-integer linear program? s.t.units of Product 1 produced units of Product 2 produced units of Product 3 produced P1, P2, P3 ≥ 0; y1, y2, y3 = 0, 1 (e) Solve the mixed-integer linear program formulated in part (d). How much of each product should be produced, and what is the projected total profit (in dollars) contribution? (P1, P2, P3, y1, y2, y3) = with profit $ .
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.
Hart Manufacturing makes three products. Each product requires manufacturing operations in three departments: A, B, and C. The labor-hour requirements, by department, are as follows.
Department | Product 1 | Product 2 | Product 3 |
---|---|---|---|
A | 1.50 | 3.00 | 2.00 |
B | 2.00 | 1.00 | 2.50 |
C | 0.25 | 0.25 | 0.25 |
During the next production period, the labor-hours available are 450 in department A, 350 in department B, and 50 in department C. The profit contributions per unit are $26 for product 1, $27 for product 2, and $31 for product 3.
(a)
Formulate a linear programming model for maximizing total profit contribution. (Let
Pi =
units of product i produced, for
i = 1, 2, 3.)
Max
s.t.Department A
Department B
Department C
P1, P2, P3 ≥ 0
(b)
Solve the linear program formulated in part (a). How much of each product should be produced, and what is the projected total profit contribution (in dollars)?
(P1, P2, P3) =
with profit $ .
(c)
After evaluating the solution obtained in part (b), one of the production supervisors noted that production setup costs had not been taken into account. She noted that setup costs are $400 for product 1, $520 for product 2, and $650 for product 3. If the solution developed in part (b) is to be used, what is the total profit contribution (in dollars) after taking into account the setup costs?
$
(d)
Management realized that the optimal product mix, taking setup costs into account, might be different from the one recommended in part (b). Formulate a mixed-integer linear program that takes setup costs into account. Management also stated that we should not consider making more than 145 units of product 1, 150 units of product 2, or 175 units of product 3. (Let
Pi =
units of product i produced and
yi
be the 0-1 variable that is one if any quantity of product i is produced and zero otherwise, for
i = 1, 2, 3.)
What is the objective function of the mixed-integer linear program?
Max
In addition to the constraints from part (a), what other constraints should be added to the mixed-integer linear program?
s.t.units of Product 1 produced
units of Product 2 produced
units of Product 3 produced
P1, P2, P3 ≥ 0; y1, y2, y3 = 0, 1
(e)
Solve the mixed-integer linear program formulated in part (d). How much of each product should be produced, and what is the projected total profit (in dollars) contribution?
(P1, P2, P3, y1, y2, y3) =
with profit $ .
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