Before they are allowed to go outside and play, they must wash the 45 windows in their house. They have 3 hours before their friends will gather in the park, and the siblings want to have as many cookies as possible when they meet their friends.
Siri can wash 6 windows in 15 minutes. Alexa can wash 5 windows in 10 minutes.
Siri makes 15 cookies in 30 minutes. Alexa makes 40 cookies in 60 minutes.
Siri can wash 6 windows in 15 minutes, which means in 3 hours (180 minutes), she can wash: 18015×6=72 windows.
Siri can also make 15 cookies in 30 minutes, which translates to: 18030×15=90 cookies.
So, Siri’s PPF might look like this:
Maximum windows washed: 72
Maximum cookies baked: 90
Alexa’s Production Possibility Frontier (PPF):
Alexa can wash 5 windows in 10 minutes, so in 3 hours, she can wash: 18010×5=90 windows.
Alexa can make 40 cookies in 60 minutes, resulting in: 18060×40=120 cookies.
Therefore, Alexa’s PPF might be represented as:
Maximum windows washed: 90
Maximum cookies baked: 120
Opportunity Costs
For Siri, the opportunity cost of each additional cookie is the number of windows she could have washed instead. So, for Siri, the opportunity cost of one cookie is 6/15 = 2/5 of a window.
For Alexa, the opportunity cost of each additional cookie is the number of windows she could have washed instead. So, for Alexa, the opportunity cost of one cookie is 5/40 = 1/8 of a window.
Equal Distribution vs. Specialization
Alexa suggests they both wash an equal number of windows, while Siri wants Alexa to wash all the windows while she makes cookies. Who is correct?
To maximize their joint output, it’s better for Alexa to wash all the windows while Siri bakes all the cookies. Here’s why:
Siri is more efficient at making cookies (90 cookies vs. Alexa’s 120 cookies).
Alexa is more efficient at washing windows (90 windows vs. Siri’s 72 windows).
So, if they specialize in their respective tasks, they can collectively produce more cookies and clean more windows, resulting in a higher overall output of both goods.
Maximum Cookies Before Going to the Park
Since they have to wash 45 windows, if they specialize as discussed above:
Siri will make 90 cookies, and Alexa will wash 45 windows.
This maximizes their output within the given time frame while fulfilling the window-washing requirement.
In this scenario, they can make 90 cookies before going to the park.
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