Problem 3: Your company produces wheel rims for heavy-duty industrial vehicles.
ID: 346604 • Letter: P
Question
Problem 3: Your company produces wheel rims for heavy-duty industrial vehicles. Each rim should weigh exactly 550 lbs. Weights as low as 544 lbs. and as high as 552 lbs. are acceptable. In 2017, the average weight of a wheel rim was 549 lbs. with a standard deviation of 0.75 lbs. What are the 3 standard deviation Cpk statistics for the upper and lower specification limits? What do these values tell you? The CEO intends to launch a new quality initiative which implies the use of six sigma-level quality when evaluating the process. How would this change your results?
Problem 4: A company is selecting among three alternative capacity plans. The first alternative is a job shop with low fixed costs ($125,000), but with highly skilled labor higher variable cost per unit ($25). The second alternative is a form of cellular manufacturing with fixed cost of $275,000 and variable cost of $18 per unit. The third consideration is a product layout. This will cost $550,000 to set up, but result in a variable cost of only $12.50 per unit. Which layout should be selected at the following volumes (a) 10,000? (b) 20,000? (c) 30,000?
Problem 5: A beverage supply company is trying to determine the appropriate stocking level for an upcoming festival to be held in town. Based on historic data, the company predicts that there is a 25% chance that the festival will attract 18,000 customers (small); a 45% chance that it will attract 35,000 (medium); a 15% chance that it will attract 50,000 (large); and a 15% chance it will attract 80,000 (huge). Assuming that each customer represents one sale of $8, what is the expected value of the festival for the company?
Explanation / Answer
Please find below answers to questions 4 and 5 :
Answer to problem 4 :
Total cost will be defined as :
Total cost = Fixed cost + Variable cost / unit x Number of units
For volume : 10000
Total cost of Job shop = $125,000 + $25 x 10,000 = $125,000 + $250,000 = $375,000
Total cost of cellular manufacturing = $275,000 + $18 x 10,000 = $275,000 + $ 180,000 = $455,000
Total cost of product layout = $550,000 + $12.50 x 10,000 = $550,000 + $125,000 = $675,000
For volume : 20,000
Total cost of Job shop = $125,000 + $25 x 20,000 = $125,000 + $500,000 = $625,000
Total cost of cellular manufacturing = $275,000 + $18 x 20,000 = $275,000 + $ 360,000 = $635,000
Total cost of product layout = $550,000 + $12.50 x 20,000 = $550,000 + $250,000 = $800,000
For volume : 30,000
Total cost of Job shop = $125,000 + $25 x 30,000 = $125,000 + $750,000 = $875,000
Total cost of cellular manufacturing = $275,000 + $18 x 30,000 = $275,000 + $ $540,000 = $815,000
Total cost of product layout = $550,000 + $12.50 x 30,000 = $550,000 + $375,000 = $925,000
Since the least cost option is to be chosen .
Job shop should be chosen for volume of 10,000 as well as 20000
Cellular manufacturing should be chosen for volume 30,000
Answer to problem 5 :
Expected number of customers can be defined as sum of “percentage sales/100 x Number of customers” for small , medium , large and huge
Therefore expected number of customers
= 0.25 x 18000 + 0.45 x 35000 + 0.15 x 50000 + 0.15 x 80000
= 4500 + 15750 + 7500 + 12000
= 39750
Expected value of the festival = $8/ customer x 39750 customers = $318000
EXPECTED VALUE OF THE FESTIVAL = $318000
EXPECTED VALUE OF THE FESTIVAL = $318000
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