Question

Consider an imperfect process that produces flour bags that follows a normal distribution, with a standard deviation of 0.8 pounds. You have been tasked with designing the process to minimize your total cost (fixing cost and filling cost). Assume that you produce 250,000 bags per year, and the cost of fixing a bag weighing more than the USL is $0.10 and the cost of fixing a bag weighing less than the LSL is $0.50. The cost of the flour is $0.15 per pound. Consider the following options for selling 5 pound bags of flour. (Round all calculations to 4 decimals, unless $ for which 2 decimals is sufficient)

Now consider eliminating the USL, what is the new total cost per year? (Use same target (mean) and LSL as in Option #1? (4 pts)

Now consider using a mean of 5.4 pounds with the LSL = 5 pounds and the USL = 6.0 pounds.

What is the filling cost per year? (4 pts)

What is the fixing cost per year? (6 pts)

What is the total cost per year? (2 pts)

What option do you recommend? (2 pts)

Answer 1

Option # 2)

Now consider eliminating the USL, what is the new total cost per year? (Use same target (mean) and LSL as in Option #1? (4 pts)

LSL = 5 pounds

z = (5-5)/0.8 = 0

P(z) = NORMSDIST(0) = 0.5

Fixing cost per year = 0.5*250000*0.5 = $ 62,500

Option # 3)

Now consider using a mean of 5.4 pounds with the LSL = 5 pounds and the USL = 6.0 pounds.

For LSL, z value = (5-5.4)/0.8 = -0.5

P(z) = NORMSDIST(-0.5) = 0.30854

Number of bags filled less than LSL = 0.30854*250000 = 77,135

For USL, z value = (6-5.4)/0.8 = 0.75

P(z) = NORMSDIST(0.75) = 0.7734

Number of bags filled more than USL = (1-0.7734)*250000 = 56,650

Fixing cost per year = 77135*0.5 + 56650*0.1 = $ 44,232.5

Filling cost per year = 250000*5.4*0.15 = $ 202,500

Total cost per year = 44232.5+202500 = $ 246,732.5