A young man plans to sell umbrellas at the city's Easter Parade. He knows that he can sell 152 umbrellas at $14 each if it rains hard, he can sell 108 if it rains lightly, and he can sell 41 if it doesn't rain at all. Past records show it rains hard 28% of the time on Easter, rains lightly 69% of the time, and does not rain at all 3% of the time. If he can buy 0, 100, or 200 umbrellas at $5 each and return the unsold ones for $3 each, how many should he buy?
A)200 umbrellas
B)100 umbrellas

Question

A young man plans to sell umbrellas at the city's Easter Parade. He knows that he can sell 152 umbrellas at $14 each if it rains hard, he can sell 108 if it rains lightly, and he can sell 41 if it doesn't rain at all. Past records show it rains hard 28% of the time on Easter, rains lightly 69% of the time, and does not rain at all 3% of the time. If he can buy 0, 100, or 200 umbrellas at $5 each and return the unsold ones for $3 each, how many should he buy? ​
A)200 umbrellas
B)100 umbrellas

Quizplus · Accepted Answer

Based on the given probabilities and sales numbers, the expected number of umbrellas sold is:

Expected sales = (0.28 x 152) + (0.69 x 108) + (0.03 x 41) = 107.76

Therefore, the seller should aim to buy around 100 umbrellas, as buying any more would result in unsold inventory that would need to be returned for a loss. The option of buying 200 umbrellas is not suitable as it is likely to result in more unsold inventory.

A Young Man Plans to Sell Umbrellas at the City's