The average time before breakdown of a machine is normally distributed and has a mean of 18 weeks and a standard deviation of three weeks. If breakdown cost averages $2,000 and preventive maintenance costs $1,400, what is the optimal preventive maintenance interval

19.24 weeks

Step-by-step explanation:

Given that;

Mean, m = 18

Standard deviation, s = 3

Break down cost = 2000

Preventive maintenance cost = 1400

The optimal preventive maintenance level is Given by :

Mean + service level * standard deviation

Service level = preventive maintenance cost / (breakdown cost + preventive maintenance cost)

Hence,

Service level = 1400/(1400+2000) = 1400 / 3400

Service level = 0.4117647

Optimal preventive maintenance level :

18 + (0.4117647 * 3)

18 + 1.2352941

= 19.235

= 19.24 weeks

y > 1/3x

y < = -x + 4

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