A farmer owns two fields of equal size that are side-by-side. One field is suitable only for growing corn and the other is suitable only for growing soybeans. (Don't ask why. :-)

The farmer can produce corn or soybeans with only one other input: labor. (Don't ask how. :-) One unit of labor is the full-time labor of a worker for an entire growing season. A worker must work for the entire season, and s/he must spend the entire season on one field or the other: her/his time can't be split across fields. (Don't ask why. :-)

The following tables record the number of bushels of output (soybeans or corn) that results from putting different numbers of workers on one of the fields for a season.

Number of workers	Corn field output (bu.)
0	0
1	100
2	180
3	240
4	280
5	300

Number of workers	Soybeans field output (bu.)
0	0
1	60
2	120
3	180
4	240
5	300

Just to be clear, if the farmer puts, say, a total of two workers on the corn field, s/he'll produce 180 bushels of corn. But s/he can't use those workers on the wheat field. If s/he has additional workers available, and s/he puts them on the soybeans field, s/he'll also produce some soybeans.

Now suppose that, the following season, the farmer still has five workers available. But s/he has acquired a second corn field. A worker can work on one corn field or the other, but not both (don't ask why :-), and it remains true that a worker who works on either corn field can't work on the soybeans field, or vice-versa.

The second corn field expands the farmer's production opportunities in a way that's a little complicated.

Suppose the farmer puts one worker on the soybeans field.

1. How many workers, total, can s/he put on the two corn fields?

2. what's the maximum amount of corn s/he can produce, in bushels?

Hint: The amount of corn produced depends on how the remaining workers are allocated across the two corn fields. For example, allocating two workers to each corn field produces a different amount of corn than allocating three workers to one field and one worker to the other. (Remember that a particular worker can work on one field or the other, but not both.)

There are two other possibilities for the amount of corn produced, in this case. These possibilities are associated with other ways of allocating the remaining workers across the two corn fields. How much corn, in bushels will the farmer produce

3. if s/he chooses the best of these two alternatives?

4. if s/he chooses the worst of these two alternatives?

Now, construct twelve ordered pairs (s, c) that represent different combinations of soybeans quantities and corn quantities the farmer could produce using the five workers and the three fields (one soybeans and two corn), depending, to some extent, on how s/he allocates workers across the two corn fields. You won't report all these ordered pairs, but I'll ask you questions about them, and you'll use them, later in this question, to construct a plot on a graph.

Hint: Start with all five workers allocated to soybeans production. Then try allocating only four workers to soybeans, then only three, etc. In cases where two or more workers are allocated to corn production, there is more than one possibility for the amount of corn produced, because there is more than one way to allocate the corn workers across the two different corn fields.

5. If the farmer doesn't allocate any workers to soybeans production, what's the maximum amount of corn s/he can produce, in bushels?

6. What's the best alternative amount (achievable with a different allocation of workers on the two corn fields)?