Zenren ElectroProducts is considering making changes in the way it procures the Z-1254 microprocessor chip. In addition to the Status Quo, which is in-house production at its current California plant, Zenren is considering either purchasing from an offshore manufacturer or making the chip in its new Arizona plant.

There are three evaluation measures (attributes) for this decision:

cost per batch of 10,000 chips,

operational ease,

and quality as measured by the number of defective chips per batch of 10,000.

For the following analysis, assume a range from $500 to $1,000 for cost per batch,

a range from 1 to 4 for the (constructed) evaluation measure scale for operational ease,

and a range from 0 to 100 for the number of defects per batch.

Note that preferences are monotonically increasing for operational ease (more is better), while preferences are monotonically decreasing for cost and number of defects (more is worse). The scores for each of the three alternatives on these three evaluation measures are as follows:

Alternatives	Cost	Operational Ease	Number of Defects
Status Quo	750	4	55
Offshore	550	1	40
Arizona	675	2	30

A multiobjective value analysis is being done to evaluate these alternatives. The single dimensional value function over cost per batch is exponential with a mid-value of 750. The single dimensional value function over operational ease is piecewise linear. The value increment going from an operational ease score of 1 to a score of 2 is the same as the value increment going from an operational ease score of 2 to a score of 3.

The value increment going from an operational ease score of 3 to a score of 4 is three times as great as the value increment going from an operational ease score of 1 to a score of 2. The single dimensional value function over number of defects per batch is exponential with a midvalue of 30. The value increment going from an operational ease score of 1 to an operational ease score of 4 is twice as great as the value increment going from a cost per batch of $1,000 to a cost of $500, while the value increment going from a number of defects per batch of 100 to a number of defects per batch of 0 is the same as the value increment going from an operational ease score of 1 to an operational ease score of 4.

(i) Show that the exponential constant for the cost-per-batch single dimensional value function is equal to infinity, while the exponential constant for the number-of-defects-per-batch single dimensional value function is equal to 55.5.

(ii) Show that the single dimensional values for operational ease scores of 2 and 3 are 0.2 and 0.4, respectively.