Given this linear programming model, solve the model and then answer the questions that follow. Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make, etc. Subject to Machine: 5x 1 + 4x 2 + 3x 3 ≤ 160 minutes Labor: 4x1 + 10x2 + 4x3 ≤ 288 hours Materials: 2x 1 + 2x2 + 4x3 ≤ 200 pounds Product 2: x2 ≤ 16 units x1, x2, x3 ≥ 0 a) Are any constraints binding? If so, which one(s)? b) If the profit on product 3 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain. c) If the profit on product 1 were changed to $22 a unit, what would the values of the decision variables be? The objective function? Explain.
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.
Given this linear programming model, solve the model and then answer the questions that follow.
Maximize Z = 12x1 + 18x2 + 15x3 where x1 = the quantity of product 1 to make,
etc.
Subject to
Machine: 5x 1 + 4x 2 + 3x 3 ≤ 160 minutes
Labor: 4x1 + 10x2 + 4x3 ≤ 288 hours
Materials: 2x 1 + 2x2 + 4x3 ≤ 200 pounds
Product 2: x2 ≤ 16 units
x1, x2, x3 ≥ 0
a) Are any constraints binding? If so, which one(s)?
b) If the profit on product 3 were changed to $22 a unit, what would the values of the decision
variables be? The objective function? Explain.
c) If the profit on product 1 were changed to $22 a unit, what would the values of the decision
variables be? The objective function? Explain.
d) If 10 hours less of labor time were available, what would the values of the decision variables
be? The objective function? Explain.
e) If the manager decided that as many as 20 units of product 2 could be produced (instead of
16), how much additional profit would be generated?
f) If profit per unit on each product increased by $1, would the optimal values of the decision
variables change? Explain. What would the optimal value of the objective function be?
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