In order to reduce costs m3 has focused on determining the

Question

M3 Manufacturing produces three distinct products; Product A, Product B, and Product C.

In order to reduce costs, M3 has focused on determining the costs associated with the quality of their three products.

Estimates of these costs were developed from last year's (2016) records, which are given below.

	Product A	Product B	Product C
NonConforming (%)	15	25	10
External Failure (%)	25	50	75
Internal Failure (%)	75	50	25

The results of this investigation are presented below.

	Product A	Product B	Product C
External Failures ($) per Unit Failed	0.97	0.32	0.17
Internal Failures ($) per Unit Failed	1.77	0.52	0.47
Appraisal ($) per Unit Produced	0.35	0.66	0.60
Prevention ($) per Unit Produced	0.30	0.18	0.44

Using the traditional quality cost model, M3 has determined the relationship between prevention cost per part (C_P) and the proportion nonconforming (p), which are given below

	Product A	Product B	Product C
Cp(p)	0.547 * 0.0183P	0.472 * 0.0212P	0.670 * 0.0149P

For this system, please assume:

• The manufacturing processes' proportion nonconforming are controllable in 1% Increments

• Only nonconforming units can fail (internally or externally)

• All nonconforming units fail (either internally or externally)

• All data is deterministic

Question 1: For Products A, B, and C, determine last year's cost per unit produced.

Question 2: For Products A, B, and C, determine the optimal (in terms of minimal cost per unit produced) proportion nonconforming and the resulting minimum cost per unit produced.