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Gnoma [55]
4 years ago
14

C&A’s potato chip filling process has a lower specification limit of 9.5 oz. and an upper specification limit of 10.5 oz. Th

e standard deviation is 0.3 oz. and the mean is 10 oz. What is the process capability index for the chip filling process?
Business
1 answer:
abruzzese [7]4 years ago
5 0

Answer:

The process capability index of the chip filling process is 0.56

Explanation:

In this question, we are asked to calculate the process capability index for the chip filing process.

To calculate this, we employ a mathematical approach.

Mathematically;

The process capability index = (upper specification limit- lower specification limit)/ 6σ

Where σ refers to the standard deviation.

From the question, we identify the following;

Upper specification limit = 10.5 oz

Lower specification limit = 9.5 oz

Standard deviation σ = 0.3

Substituting these in the equation, we have;

(10.5-9.5)/6(0.3) = 1/1.8 = 0.56

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Complete Question:

Suppose a firm has two types of customers but cannot tell which type of buyer a customer is before a purchase is made. One group of customers has an inverse demand of P = 100 – 10Q, while another group of customers has an inverse demand curve of P = 110 – 22.5Q. If the firm wanted to use a quantity discount pricing scheme, what prices should it set? Assume that the marginal cost of production is constant at $20.

A) The firm could charge $65 per unit for any quantity purchased or $60 per unit if buying 4 or more units.

B) The firm could charge $50 per unit for any quantity purchased or $40 per unit if buying 8 or more units.

C) The firm could charge $25 per unit for any quantity purchased or $20 per unit if buying 2 or more units.

D) The firm could charge $85 per unit for any quantity purchased or $75 per unit if buying 6 or more units.

Answer:

Option A. The firm could charge $65 per unit for any quantity purchased or $60 per unit if buying 4 or more units.

Explanation:

<u>Group One Customers:</u>

We will find the price and quantity by using the following relationship:

Marginal Revenue = Marginal Cost

But the first step would be to calculate marginal revenue.

<u>Step1: Calculate Marginal Revenue</u>

The price and quantity relation of group one customers is given as under:

P = 100 - 10Q

Now we will use total revenue equation which is given as under:

Revenue = Price * Quantity

Here

Price = 100 - 10Q

By putting this in the above equation, we have:

Revenue = (100 - 10Q) * Q

Revenue = 100Q - 10Q^2

Taking derivative on both sides we have:

Marginal Revenue = 100 - 2*10*Q = 100 - 20Q

Now as we know that:

Marginal Revenue = Marginal Cost

Here

Marginal Revenue = 100 - 20Q

Marginal  Cost = $20

By putting values, we have:

$100 - 20Q  =  $20

$100 - $20 = 20Q

Q = $80 / $20  = <u>4 Units</u>

Now putting this value in the price equation we have:

Price = $100 - 10*4 = <u>$60</u>

<u>Group Two Customers:</u>

We will find the price and quantity by using the following relationship:

Marginal Revenue = Marginal Cost

But the first step would be to calculate marginal revenue.

<u>Step1: Calculate Marginal Revenue</u>

The price and quantity relation of group one customers is given as under:

P = 110 – 22.5Q

Now we will use total revenue equation which is given as under:

Revenue = Price * Quantity

Here

Price = 110 - 22.5Q

By putting this in the above equation, we have:

Revenue = (110 - 22.5Q) * Q

Revenue = 110Q - 22.5Q^2

Taking derivative on both sides we have:

Marginal Revenue = 110 - 2*22.5*Q

Marginal Revenue = 110 - 45Q

Now as we know that:

Marginal Revenue = Marginal Cost

Here

Marginal Revenue = 110 - 45Q

Marginal  Cost = $20

By putting values, we have:

$110 - 45Q  =  $20

$110 - $20 = 45Q

Q = $90 / $45  = <u>2 Units</u>

Now putting this value in the price equation we have:

Price = $110 - 22.5*2 = <u>$65</u>

<u></u>

<h2><u>The data extracted from the above two scenario is as under:</u></h2><h2><u>For Group 1, Price is $60 and Quantity is 4 Units</u></h2><h2><u>For Group 2, Price is $65 and Quantity is 2 Units</u></h2><h2><u>Hence the option A is correct.</u></h2>
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