You have a retail-clothing store for fashion items. For simplicity, let us consider just one gown in this question. You have to purchase your inventory at the start of the season at $60 per gown, and you plan to sell it $100. You have a 50% chance of selling more than 10 gowns.

If you have to literally throw out unsold gowns at the end of the season, how much inventory will you order?

However there is an active post-season sales market where you can sell gowns for $B (B stands for ‘bargain’ sales). Plot on a graph the number you should order for values of B from $0 to $50.

To calculate how much inventory to order, we need to consider the probability of selling more than 10 gowns and the potential profit or loss from the post-season sales market.

Let's break down the scenario step by step:

Step 1: Calculate the probability of selling more than 10 gowns.
The probability of selling more than 10 gowns can be calculated using a binomial distribution. In this case, we have a 50% chance, so the probability would be 0.5. However, since we are considering just one gown, the probability would be the chance of selling 1 or more gowns. This would be inverse of the probability of not selling any gowns, which is (1-0.5) = 0.5 or 50%.

Step 2: Calculate the potential profit or loss from post-season sales.
Given the active post-season sales market, we need to consider the potential profit or loss from selling the unsold gowns. Let's denote the price of post-season sales as $B. If we don't sell a gown during the regular season, we can sell it in the post-season at a reduced price. The profit or loss would depend on the difference between the purchase price ($60) and the post-season sale price ($B). If $B is less than $60, we would incur a loss. If $B is greater than $60, we would make a profit.

Step 3: Determine the inventory order quantity for different values of B.
To determine the inventory order quantity, we need to weigh the potential profit or loss in the post-season sales with the probability of selling more than 10 gowns. We can plot this on a graph for different values of B, from $0 to $50.

The equation to calculate the expected profit or loss per gown (EPL) for each value of B is as follows:

EPL = (probability of selling more than 10 gowns * profit per gown from regular season) + (probability of not selling any gowns * loss per gown from post-season sales)

Let's calculate the inventory order quantities and plot them on a graph for B from $0 to $50.