**IKEA’s Poäng Chairs (for Q4-5)**

Poäng chair is one of IKEA’s most popular products. Average weekly sales of this chair in each store is Normal with mean 20 units and standard deviation of 10 units. Each chair costs IKEA $10 to produce and is sold at a price $60.  You are managing the inventory of Poäng chairs at two locations: Mega Bang Na and EmSphere stores.

**Q4.**  If you order the inventory independently for each store, what is the total number of chairs to order each week across the two stores? Round up to the next integer.

To determine the total number of Poäng chairs to order each week across the two stores, we need to calculate the expected total demand for both Mega Bang Na and EmSphere.

Since weekly demand in each store is normally distributed with:
- Mean $ \mu = 20 $ units
- Standard deviation $ \sigma = 10 $ units

Given that demand in each store is independent, the distribution of total demand for both stores will be the sum of two independent normal distributions.

### Step 1: Mean of the Total Demand
For two independent normal variables $ X $ and $ Y $, if:
- $ X \sim N(\mu_X, \sigma_X^2) $
- $ Y \sim N(\mu_Y, \sigma_Y^2) $

Then, the sum $ Z = X + Y $ will also be normally distributed with:
- Mean $ \mu_Z = \mu_X + \mu_Y $
- Variance $ \sigma_Z^2 = \sigma_X^2 + \sigma_Y^2 $

In this case:
- Mean demand for each store, $ \mu = 20 $
- Total mean demand for two stores, $ \mu_Z = 20 + 20 = 40 $

### Step 2: Standard Deviation of the Total Demand
- Standard deviation for each store, $ \sigma = 10 $
- Variance for each store, $ \sigma^2 = 10^2 = 100 $
- Total variance for both stores, $ \sigma_Z^2 = 100 + 100 = 200 $
- Total standard deviation, $ \sigma_Z = \sqrt{200} = 10\sqrt{2} \approx 14.14 $

### Step 3: Expected Total Demand
Since we are asked to order the **total number of chairs** each week, we can use the mean of the total distribution:
\[
\text{Expected total demand} = 40
\]

Since we need to **round up to the next integer**, the total number of chairs to order each week across both stores is:
\[
\text{Total Order Quantity} = \lceil 40 \rceil = 40
\]

### Final Answer:
**Order 40 chairs per week across the two stores.**

Would you like more details on this solution, or do you have any questions?

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Here are 5 related questions to deepen your understanding:
1. How would the answer change if the standard deviation was 20 units instead of 10?
2. What would be the total weekly revenue from both stores based on this average demand?
3. How would demand variability affect weekly sales planning if the stores shared inventory?
4. How could you calculate the probability of selling at least 50 chairs in a given week across both stores?
5. What considerations might go into setting a reorder point for these chairs based on weekly demand?

**Tip:** When working with sums of independent normal distributions, remember that the resulting distribution will also be normal, with a mean and variance that are the sum of the individual means and variances.

If you order the inventory independently for each store, what is the total number of chairs to order each week across the two stores?

Discover how to calculate the total weekly inventory order for IKEA's Poäng chairs across two stores. Based on normal distribution statistics, the mean demand is 40 chairs per week, with a standard deviation of 14.14. Ideal for students in Grades 11-12 studying statistics and inventory management.

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