Question

SoleMate’s Burkins sneakers cost $40 per pair from the supplier and are sold by SoleMate at $80 per pair during their peak fall selling season. Shoes not sold during the fall are moved to the SoleMate outlet store and sold at the discounted price of $25. The demand is normally distributed with a mean of 100 and standard deviation of 20. What is the optimum order quantity? Choose the closest answer. a) 100 b) 105 c) 110 d) 115

Answer 1

Selling price(SP) = $80

Cost price (CP) = $40

Salvage value(V) = $25

Average demand (d) = 100

Standard deviation of demand (d) = 20

Overage cost(Co) = CP - V = $40-$25 = $15

Underage cost(Cu) = SP-CP = $80-$40 = $40

Service level = Cu/(Co + Cu) = 40/(15+40) = 40/55 = 0.727 = 72.7%

So the optimal service level is 72.7%

At 72.7% service level value of Z = 0.61 (derived from the standard normal table)

Optimum order quantity = d + Z x d

= 100 + (0.61 x 20)

= 100 + 12.2

= 112.2 or rounded up to 112

The option that is closest to 112 is 110.so the answer is option c