Jeff sells the New York Times Sunday newspaper at a city corner near several churches. He sells each newspaper for $6.50 after purchasing them for $4.00. Any unsold newspaper can be returned to the New York Times for a $0.75 credit. Jeff expects demand on Sunday to be 75, 100, 125, or 150 newspapers and would like to order one of these four quantities from the New York Times. If the Jeff uses the maximin criterion, how many newspapers will he order?

Question

Quizplus · Accepted Answer

The maximin criterion involves selecting the action that has the highest minimum payoff. For Jeff, the minimum payoff occurs when he orders more newspapers than he can sell, as unsold newspapers only return $0.75 each, compared to a profit of $2.50 ($6.50 - $4.00) for each sold newspaper. The minimum payoff for each order size is as follows:- Ordering 75 newspapers: The worst-case scenario is selling all 75, resulting in a profit of 75 * $2.50 = $187.50.- Ordering 100 newspapers: If only 75 are sold, he makes $187.50 on the sold ones and gets a credit of $0.75 for each of the 25 unsold, totaling $18.75. So, the minimum payoff is $187.50 + $18.75 = $206.25.- Ordering 125 newspapers: If only 75 are sold, he makes $187.50 on the sold ones and gets a credit of $0.75 for each of the 50 unsold, totaling $37.50. So, the minimum payoff is $187.50 + $37.50 = $225.- Ordering 150 newspapers: If only 75 are sold, he makes $187.50 on the sold ones and gets a credit of $0.75 for each of the 75 unsold, totaling $56.25. So, the minimum payoff is $187.50 + $56.25 = $243.75.However, the maximin criterion focuses on the highest of these minimum payoffs, which means Jeff would choose the option with the least potential loss or the smallest negative impact, which is when he orders the least amount of newspapers (75), ensuring he has no unsold stock and thus no need to rely on the lower return from unsold newspapers. This approach minimizes potential losses, aligning with the maximin strategy of avoiding the worst-case scenario.

Jeff Sells the New York Times Sunday Newspaper at a City