Kyle store sells K2 skis. The store makes a $200 profit per unit sold during the ski season, but it should take a $50 loss per unit if sold after the season is over. The following discrete probability distribution has been estimated for the season's demand.
$$\begin{array} { | c | c | }
\hline \text { Demand } ( D ) & \text { Demand Probability } \
\hline 10 & 0.1 \
20 & 0.3 \
30 & 0.3 \
40 & 0.2 \
50 & 0.1 \
\hline
\end{array}$$
-Use the information in Scenario D.2..What is the best order quantity?
A) Fewer than or equal to 20 units
B) Greater than 20 units but fewer than or equal to 40 units
C) Greater than 40 units but fewer than or equal to 50 units
D) Greater than 50 units

Question

Kyle store sells K2 skis. The store makes a $200 profit per unit sold during the ski season, but it should take a $50 loss per unit if sold after the season is over. The following discrete probability distribution has been estimated for the season's demand.
 $$\begin{array} { | c | c | } 
\hline \text { Demand } ( D ) & \text { Demand Probability } \
\hline 10 & 0.1 \
20 & 0.3 \
30 & 0.3 \
40 & 0.2 \
50 & 0.1 \
\hline
\end{array}$$
-Use the information in Scenario D.2..What is the best order quantity?
A) Fewer than or equal to 20 units
B) Greater than 20 units but fewer than or equal to 40 units
C) Greater than 40 units but fewer than or equal to 50 units
D) Greater than 50 units

Quizplus · Accepted Answer

To determine the best order quantity, we need to calculate the expected profit for each possible order quantity. Let Q be the order quantity. If Q is greater than the demand, the excess inventory will be sold at a loss of $50 per unit. If Q is less than the demand, the store will lose out on potential profits. Therefore, the expected profit can be expressed as:

Expected Profit = (Demand ≤ Q) * ($200 profit) + (Demand > Q) * ($200 profit - $50 loss)

Using the probability distribution given, we can calculate the expected profit for each possible order quantity:

Q = 10: Expected Profit = 0.1 * ($200) + 0.9 * ($200 - $50) = $175
Q = 20: Expected Profit = 0.4 * ($200) + 0.6 * ($200 - $50) = $170
Q = 30: Expected Profit = 0.7 * ($200) + 0.3 * ($200 - $50) = $185
Q = 40: Expected Profit = 0.9 * ($200) + 0.1 * ($200 - $50) = $195
Q = 50: Expected Profit = 1.0 * ($200) = $200

Based on this calculation, the best order quantity is between 20 and 40 units, with an expected profit of either $170 or $195. However, we cannot determine whether the best order quantity is 20, 30, or 40 without additional information about the store's carrying and ordering costs.

Kyle Store Sells K2 Skis -Use the Information in Scenario D