# Solving linear programming question

1. A component has a reliability of 0.75. How many identical components do we have to add n parallel to the frst to increase the overall reliability to 0.95?

You may use the following general formulas

R_sys = 1-(1-R1)(1-R2)...(1-Ri)...(1-Rn)

Ri=e^-(lamda*t)

2. Find both the minimum and maximum values of U=6x1+10x2+7 (graphically) subject to the constrains 2x1+5x2<=24, x1>=0, and x2>=0

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#### Solution Preview

1. Let n be the number of identical components, we will start with n=1 until conditions satisfy.

When n=1, Rsys=1-(1-0.75)=0.75. No, it is less than 0.95.

When n=2, Rsys=1-(1-0.75)(1-0.75)=0.9375. No, it is less than ...

#### Solution Summary

The solution gives detailed steps on solving a linear programming question using graphic method.

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