# 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.

Linear Programming for Optimal Solutions and Functions

Consider the following linear programming problem:

Min A + 2B

s.t.

A +4B is less than or equal to 21

2A+B is greater than or equal to 7

3A+1.5B is less than or equal to 21

-2A + 6B is greater than or equal to 0

A,B is greater than or equal to 0

1. Find the optimal solution using the graphical solution procedure and the value of the objective function??

2. Suppose the objective function is changed to max 5A + 2B. Find the optimal solution and the value of the objective function??

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