Question

In: Operations Management

Q3: Consider a seller of Christmas trees at a unit price of 30 dollars. He purchases...

Q3: Consider a seller of Christmas trees at a unit price of 30 dollars. He purchases the trees
from a farm for 10 dollars each. Transportation of a tree from the farm to the seller costs 2
dollars per tree. The seller takes an imputed entrepreneurial salary of 10,000 dollars into
account. Every season, he has to pay a rent of 2,000 dollars for his store. Unsold trees have to
be processed to sawdust at the cost of 1 dollar for a single tree. If the seller is out of stock he
will satisfy customer demand by ordering an additional tree from another nearby seller at a
cost of 62 dollars per tree, including transportation. Demand for Christmas trees during the season is assumed to be normally distributed with mean 10,510 units and standard deviation of 2,114 units. What is the optimal number of Christmas trees to order this year?

Solutions

Expert Solution

Selling price, p = $30

Cost of the tree from farm, c = $12 (Including transport)

Cost of the tree from nearby seller, s = $62

Cost of sawdust process, Cp = $1

Cost of understocking, Cu = s-p = $32 (We pay $32 extra for not having optimal stock of tree from farms and fulfilling the demand from the nearby seller)

Cost of overstocking, Co = c + Cp = $13 (If we have extra trees, we pay $12 to procure and $1 to process them to sawdust)

Critical ratio = Cu / (Cu + Co) = 32 / 45 = 0.7111

Z = 0.56 for Critical ratio = 0.711 (Refer standard normal distribution table)

optimal number of Christmas trees to order this year = Mean + Z*Std deviation = 10510 + 0.56*2114 =11693.84 or 11694

keosha answered 2 years ago
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