Linear Programming Used to Attain Optimum Solutions

1.1) An Operations Manager would like to understand how linear programming (LP) can be used to attain optimum solutions when allocating scarce organizational resources. He/She has the following questions:

a) What is LP? How is an LP problem defined
b) Define objective function, constraint, and decision variable
c) Our firm makes two products: Y and Z. Suppose that each unity of Y costs $10 and sells for $40. Each unit of Z costs $5 and sells for $25. If the firm's goal were to maximize profit, what is the appropriate objective function?
d) An LP problem must be "solved." One solution method is the corner point solution. How is this method applied? What gets solved in an LP problem? Are other solution methodologies available.

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Answer:
Linear programming (LP) can be defined as a mathematical technique for determining the optimal allocation of resources and obtaining a particular objective that may be profit maximization or cost minimization, when there are alternative uses of resources like money, manpower, material or machine.
In linear programming technique the total effectiveness of the problem can be expressed as a linear function of individual allocations and the limitations on resources give rise to linear equalities or inequalities of the ...

Solution Summary

The solution discusses linear programming used to attain optimum solutions.

... value of the objective function is attained at the ... The expert finds the optimal solution using the graphical ... Consider the following linear programming problem: ...

... d. Use the graphical method to solve the problem ... 2) The output of the linear programming problem using Excel solver is ... Not Binding 1 $D$11 Benefit 3 Used 126 $D ...

... The solution uses the simplex method to solve the dual problem. ... a. Set up the dual of the above linear program. ... c. Use your work in (b) to give an optimal...

... the optimal solution to the integer linear programming problem ... and-bound method (for integer programming problem) x1 ... amount of the 3 ingredients used to produce ...

Linear Programming : Optimal Solution. ... A LP problem is solved using a graphical method. ... Z = 3x1 + 5x2 To find the maximum value, we need to use the corner point ...

... on the context in which they are used. ... This drawback of linear/integer programming is addressed ... a more efficient solution for goal programming Ranking of ...

...Use this value as constraint in next level ...Solution contains formulation of a linear programming model to ... words produced and sold are used because there ...

... Avoid the use of overtime given the low ... a. Formulate a linear programming model to determine the ... produced, the annual profit contribution attained, and the ...

... Thanks for using BrainMass. ... 1. Consider the following linear programming problem Max 8X + 7Y. ... To find the maximum value, we need to use the corner point theorem ...