Store A uses the newsvendor model to manage its inventory. Demand for its product is normally distributed with a mean of 500 and a standard deviation of 300. Store A purchases the product for $10 each unit and sells each for $25. Inventory is salvaged for $5. What is its maximum profit? $12,500 $8000 $5000 $7500

The newsvendor model is a statistical model used to manage inventory and determine the appropriate amount of inventory. So first of all we determine the optimal inventory level then we use it to find maximum profit. In order to determine optimal inventory level we first have to find possible variability in demand, for that we use the critical fractile formula which is as follows:

f= cu/cu+co

cu= underage cost = price - cost = $25 -$10 = $15

co= overage cost = cost - salvage value = $10 -$5 = $5

f= 15/15+5

f= 0.75

If we look at the standard normal cumulative distribution table 0.75 is equal to z= 0.67.

Q = Mean+ (z* standard deviation)

Optimal inventory = 500 + (0.67* 300)

Optimal inventory = 701 units

WE ROUND OFF THE UNITS TO 700.

Now we calculate maximum profit as follows:

maximum profit = contribution * Q

maximum profit = ($25 - $10) * 700

maximum profit = 10500