Question

A farmer can plant corn (x) and soybeans (y). He has at most 200 acres of land. Corn requires 2 acres per field, and soybeans require 1 acre per field. He needs to plant at least 50 total fields of crops.



Which ordered pair (x,y) represents a possible planting combination the farmer could choose?


(30,10)


(60,20)


(50,100)


(80,40)

Answer 1

Let x = number of corn fields and y = number of soybean fields. Constraints:
- Land: 2x + y ≤ 200
- Fields: x + y ≥ 50

Check each pair:
- (30,10): 2(30)+10 = 70 ≤ 200, but 30+10 = 40 < 50 → not allowed.
- (60,20): 2(60)+20 = 140 ≤ 200 and 60+20 = 80 ≥ 50 → allowed.
- (50,100): 2(50)+100 = 200 ≤ 200 and 50+100 = 150 ≥ 50 → allowed.
- (80,40): 2(80)+40 = 200 ≤ 200 and 80+40 = 120 ≥ 50 → allowed.

So any of (60,20), (50,100), or (80,40) is a possible planting combination (but (30,10) is not).