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wariber [46]
3 years ago
11

A company produces a product with the upper specification limit of 22 inches long and the lower specification limit of 18 inches

. The process that produces the product has an average length of 19 inches with a standard deviation of 0.4 inches. What is the process capability ratio/index
Business
1 answer:
kotegsom [21]3 years ago
8 0

Answer:

0.83

Explanation:

Given that ;

the upper specification limit USL = 22 inches

the  lower specification limit LSL =  18 inches.

Mean average length \bar X =  19 inches

Standard deviation \sigma  = 0.4 inches

The process capability ratio/index C_{pk= Min[\dfrac{USL - \bar X}{3(\sigma)}, \dfrac{\bar X - LSL}{3( \sigma)}]

C_{pk= Min[\dfrac{22 - 19}{3(0.4)}, \dfrac{19- 18}{3( 0.4)}]\\

C_{pk }= Min[\dfrac{3}{1.2}, \dfrac{1}{1.2}]\\

C_{pk }= Min[2.5  \ ,\ 0.83]\\

The process capability ratio/index = 0.83

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erik [133]

Answer:

The weekly revenue is maximum at x=1.67.

Explanation:

The given function is

f(x)=1000x -300x^2         .... (1)

where, f(x) is the total revenue at price x.

We need to find the price x at which the weekly revenue is maximum.

The leading coefficient of the given function is -300, which is a negative number. So, it is a downward parabola and vertex of a downward parabola is the the point of maxima.

If a parabola is defined as

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then the vertex of the function is

(-\frac{b}{2a},g(-\frac{b}{2a}))

From (1) and (2) it is clear that

a=-300,b=1000, c=0

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-\frac{b}{2a}\approx 1.67

Therefore the weekly revenue is maximum at x=1.67.

4 0
3 years ago
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