Question

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

Answer 1

The maximum profit using the newsvendor model for Store A is $7,500. The correct option is the last option.

The Breakdown

To determine the maximum profit using the newsvendor model, we need to calculate the optimal order quantity that maximizes expected profit.

Given:

Mean demand (μ) = 500

Standard deviation of demand (σ) = 300

Purchase cost per unit (c) = $10

Selling price per unit (p) = $25

Salvage value per unit (s) = $5

The newsvendor model assumes that excess demand is lost sales and unsold inventory is salvaged at the salvage value.

The optimal order quantity (Q*) can be calculated using the following formula:

Q* = μ + (Z × σ)

Where:

Z is the z-score corresponding to the desired service level. For simplicity, let's assume a service level of 50%, which corresponds to a z-score of 0.

Q* = 500 + (0 × 300)

Q* = 500

Now, let's calculate the expected profit (π) using the optimal order quantity:

π = (p - c) × min(Q*, μ) + (s - c) × max(0, Q* - μ)

π = ($25 - $10) × min(500, 500) + ($5 - $10) × max(0, 500 - 500)

π = $15 × 500 + (-$5) × 0

π = $7,500

Therefore, the maximum profit using the newsvendor model for Store A is $7,500.

Answer 2

maximum profit = 10500

Step-by-step explanation:

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