Question

Tony wants to plant at least 40 acres of corn and at least 50 acres of soybeans. He wants no more than 200 acres of corn and soybeans. Show and describe all the possible combinations of the number of acres and of soybeans Tony could plant. List two possible combinations.

Answer 1

Combination one is Tony could plan 120 acres of corn , and 50 acres of soybeans. This would equal a total of 170 acres, so no more than 200 acres. Combination two is Tony could plant 40 acres of corn, and 150 acres of soybeans. This would equal 190 acres so no more than 200 acres.

Answer 2

let
x------------------- >acres of corn
y------------------- >acres of soybeans
we have that
x>=40
y>=50
and
x+y <= 200------------------ > y <= 200-x

using a graph tool
see the solution in the attached figure

the solution is the triangle formed with the point ABC
A(40,50) -------- > minimum acres of corn (40) and minimum acres of soybeans (50)
B(40,160) -------> minimum acres of corn (40) and maximum acres of soybeans (160)
C(150,50) ------ > maximum acres of corn (150) and minimum acres of soybeans (50)

List two possible combinations

see the graph
point (100,100)---> acres of corn 100 and acres of soybeans 100
point (50,150)---> acres of corn 50 and acres of soybeans 150