Response:
Bob’s best approach is to prepare for sunny conditions, unless he can access a weather forecast for the next day.
Explanation in detail:
This scenario focuses on the potential for gains versus the risk of losses. We will evaluate the options available to Bob in different weather situations.
When Bob buys for rain:
He purchases 500 umbrellas priced at $5 each, leading to a total expenditure of $2500.
In the event of rain, Bob can sell all umbrellas at $10 each, yielding total revenue of $5000. Consequently, his maximum profit equals $2500. Recall that:
Profit = Revenue - Cost
If the weather is sunny, he will only manage to sell 100 umbrellas for $10 each, resulting in a revenue of $1000. Therefore, in this scenario, he faces a maximum profit of -$1500. This indicates that his minimum loss in this case is $1500.
When Bob prepares for Shine:
He opts for purchasing 100 umbrellas at $5 each and 1000 sunglasses at $2 each, totaling an expense of $2500.
On a sunny day, he can sell all umbrellas for $10 each and all sunglasses for $5. This allows him to achieve a total revenue of $6000. Thus, his maximum profit amounts to $3500.
Conversely, during rain, Bob can only dispose of 100 umbrellas at $10 each, but he sells none of the sunglasses, yielding a maximum profit of $1000. Here, the maximum profit still evaluates to -$1500, meaning his minimum loss remains $1500.
In both scenarios, the worst possible outcome for Bob is consistent: a loss of $1500.
However, in the most favorable scenario, purchasing for sunny conditions results in higher profits. Therefore, if the risks are equivalent, it is more advantageous to adopt the strategy that provides greater profitability.
