Question

k Plus hapter 2 Assignment He 4 Susan can pick 4 pounds of coffee beans in an hour or gather 2 pounds of nuts. Tom can pick 2 pounds of coffee beans in an hour or er 4 pounds of nuts. Each works 6 hours per day. a. Together, what is the maximum number of pounds of coffee beans the two can pick in a day? What is the maximum number of pounds of nuts the two can gather in a day? Maximum amount of coffee beans: Maximum amount of nuts: 3 pounds per day b. Now suppose Susan and Tom were gathering the maximum number of pounds of nuts when they decided that they would like to begin picking 8 pounds of coffee beans per day who would pick the coffee beans,Susan ' pounds per day Print How many pounds of nuts would they still be able to gather?pounds of nuts per day be possible for Susan and Tom in total to gather 26 pounds of nuts and pick 20 pounds of coffee beans each day? Yes If so, how much of each good should each person pick? Coffee Beans Nuts Tom pounds pounds

Answer 1

Solution:

In an hour,

Susan can pick either 4 pounds of coffee beans or 2 pounds of nuts.

Tom can pick either 2 pounds of coffee beans or 4 pounds of nuts.

Then, in a day with 6 hours (on the extremes),

Susan can pick either (6*4=) 24 pounds of coffee beans or (6*2=) 12 pounds of nuts.

Tom can pick either (6*2=) 12 pounds of coffee beans or (6*4=) 24 pounds of nuts.

a) So, in a day, together Susan and Tom can pick

Maximum pounds of coffee beans = 24 + 12 = 36 pounds

Maximum pounds of nuts = 12 + 24 = 36 pounds

b) Clearly, in an hour, Susan can gather more pounds of coffee beans than Tom (4 > 2), thus, Susan has a comparative advantage in picking coffee beans.

Susan should pick the coffee beans.

Since Susan takes an hour to gather 4 pounds of coffee beans, to gather 8 pounds of coffee beans, she'll need to devote 2 hours of her day towards coffee beans gathering. Now, she still is left with (6-2=) 4 hours, which can be used to gather nuts. In 4 hours, Susan can gather 4*2= 8 pounds of nuts.

Furthermore, Tom still gives his entire day to nut collection, so he gathers 24 pounds of nuts (as already noted in introductory part before part (a)). So, together they would still be able to gather (8+24=) 32 pounds of nuts.

c) Yes, picking 26 pounds of nuts and 20 pounds of coffee beans in total each day is possible. This is how:

As already noted, since Susan specialize in coffee beans picking and Tom specialize in nut picking, this combination is achievable is Tom does what he specializes in, that is give his entire day to nut collection. So, this way 24 pounds of nuts can be gathered.

Similarly, Susan can devote her most time in what she specializes in. Achieving this combination requires from Susan to collect 20 pounds of coffee beans and 2 pounds of nuts. So, if she devotes 5 hours in coffee beans collection (gathering 5*4= 20 pounds of it) and 1 hour in nut collection (gathering 1*2= 2 pounds of it), this combination can be achieved. Hence, we have the following table:

	Coffee beans	Nuts
Tom	0 pounds	24 pounds
Susan	20 pounds	2 pounds

d) In similar way as in above part, we can say that a combination of 30 pounds of coffee beans and 12 pounds of nuts is attainable. This happens when Susan collects only coffee beans (thus, collecting 24 pounds of coffee beans by devoting all 6 hours to it) and Tom collects a combination of both items (devoting 3 hours to coffee beans collection, thereby gathering 3*2=6 pounds of coffee beans and devoting remaining 3 hours to nut collection, thereby gathering 3*4= 12 pounds of nuts).