Question

Russell's Independent Book Store is trying to decide on how many copies of a book to purchase at the start of the upcoming selling season. The book retails at $40.00. The publisher sells the book to Rusell at $20.00. Rusell will dispose of all of the unsold copies of the book at $15, at the end of the season. Rusell estimates that demand for this book during the season is Normal with a mean of 1000 and a standard deviation of 250.

A)Find the critical ratio CR?

B)Find order quantity Q to maximize expected profit?

C) Find the maximum profit?

D) Find mismatch cost by using the maximum profit value found in C and CV-CR table?

Answer 1

Underage cost, Cu = p - c = 40 - 20 = $ 20

Overage cost, Co = p - v = 20 - 15 = $ 5

A)

Critical ratio, CR = Cu/(Cu+Co)

= 20/(20+5)

= 0.8

B)

z value = NORMSINV(0.8) = 0.8416

Optimal order quantity, Q = mean + z*std dev

= 1000+0.8416*250

= 1,210 copies

C) Maximum profit = mean demand * Cu

= 1000*20

= $ 20,000

D)

From standard normal loss table, for z=0.8416, I(z) = 0953

Expected Leftover inventory, V = 250*0.953 = 238

Expected sales, S = Q-V = 1210-238 = 972

Expected profit = S*Cu - V*Co = 972*20 - 238*5 = 18,250

Mismatch cost = Maximum profit - Expected profit

= 20000 - 18250

= $ 1,750