Operations research linear model question

In summary, the Dean's Furniture Company assembles regular and deluxe kitchen cabinets from precut lumber. The daily capacity of the assembly department is 200 regular cabinets and 150 deluxe. Varnishing a deluxe unit takes twice as much time as painting a regular one. If the painting/varnishing department is dedicated to deluxe units only, it can complete 180 units daily. The company estimates that the revenues per unit for the regular and deluxe cabinets are 100 and 140, respectively. The objective function is Max z = 100x1 + 140x2, with x1 representing the number of regular cabinets and x2 representing the number of deluxe cabinets. The constraints are x1 <= 200, x2 <= 150
  • #1
andrassy
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0

Homework Statement

Dean's Furniture Company assembles regular and deluxe kitchen cabinets from precut lumber. The regular cabinets are painted white, and the deluxe are varnished. Both painting and varnishing are carried out in one department. The daily capacity of the assembly department is 200 regular cabinets and 150 deluxe. Varnishing a deluxe unit takes twice as much time as painting a regular one. If the painting/cvarnishing department is dedicated to deluxe units only, it can complete 180 units daily. The company estimates that the revenues per unit for the regular and deluxe cabinets are 100 and 140, respectively. Find the optimal schedule per day.


The Attempt at a Solution

So I made my objective function Max z = 100x1 + 140x2 where x1 is the number of regular cabinets to produce and x2 is the amount of deluxe. My constrictions, however, I am unsure to model. It appears that x1 <= 200 and x2<=150 but then there is the part about deluxe only can make 180 and it takes twice as long to make a deluxe, neither of which I am sure how to model in the constrictions. Any suggestions?
 
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  • #2
hi Andrassy..
gd evening.. hope u r fine and doing well n ur life..
mmmmm.. i was wondering did u know how 2 solve this problem at the end..?!
 

What is operations research linear model?

The operations research linear model is a mathematical approach used to optimize complex systems. It involves the use of mathematical and statistical techniques to solve problems in decision-making, resource allocation, and planning.

What are the key components of a linear model?

The key components of a linear model include decision variables, constraints, objective function, and parameters. Decision variables represent the choices to be made, constraints limit the feasible solutions, and the objective function defines the goal or objective of the model. Parameters are numerical values used in the model to represent real-world quantities.

What are the applications of operations research linear model?

The operations research linear model has various applications in different fields, such as supply chain management, transportation planning, finance, marketing, and healthcare. It can be used to optimize production processes, allocate resources efficiently, and make data-driven decisions.

What is the difference between a linear model and a non-linear model?

The main difference between a linear model and a non-linear model is the form of the mathematical equations used. In a linear model, the relationships between variables are described by linear equations, whereas in a non-linear model, the relationships are described by non-linear equations. This makes the solution process and interpretation of results different for each type of model.

How is sensitivity analysis used in operations research linear model?

Sensitivity analysis is used in operations research linear model to determine the impact of changes in the input parameters on the optimal solution. It helps in understanding the stability and robustness of the model and can be used to identify critical parameters that significantly affect the solution. This analysis can also help in making informed decisions in uncertain situations.

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