Please consider the data for SKUs X, Y, and Z. The store currently carries SKUs X and Y. The store manager considers discontinuing SKUs X and Y in favor of a new SKU Z, expecting that all consumers will be willing to switch from X/Y to Z. Please answer the following questions to help him decide (assuming a managerial R,Q policy is in place):

a) What is the minimum degree of substitutability (g) between SKUs X and Z as well as between SKUs Y and Z, respectively, that must be achieved to maintain profits after SKU rationalization at the same level as before SKU rationalization?

b) Let the true degree of substitutability be 92%. How will total profits change (in $ terms) after SKU rationalization?

c) If the degree of substitution is 92%, how will total inventories (the sum of cycle stocks and safety stocks) change after SKU rationalization?

d) Explain the THREE reasons for the inventory reduction identified in Q.1c above.