Question

Trees in urban areas help keep air fresh by absorbing carbon dioxide. A city has $2100 to spend on planting spruce and maple trees. The land available for planting is 45,000 square feet. Spruce trees cost $30 to plant and require 600 square feet of space. Maple trees cost $40 to plant and require 900 square feet of space. Spruce trees absorb 650 lb/yr of carbon dioxide and maple trees absorb 300 lb/yr of carbon dioxide. How many of each tree should the city plant to maximize carbon dioxide absorption?

Answer 1

X= number of spruce trees
Y= number of maple tree
30x+40y ≤ 2100
600x+900y≤ 45000
0≤x
0≤y
(Plot this on a graphing calculator or Desmos)
I plotted this and got my restraints as such:
(0,0), (0,50)(70,0)(30,30)
To solve pug into this expression: 650x+300y
The highest answer will be the answer
(0,0)=0
50*300 <70*650 for sure.
70*650=45500
(30*650=19500) + (30*300=9000)=28500.
The answer is 70 spruce trees.
Check:
2100 is greater than or equal to 30(70) (yes, equal)
45000 is greater than or equal to 600(70) (yes-42000)
x=0 or greater (yes, 70)
y=0 or greater (yes, equal)

To maximize profits, the city should plant 70 spruce trees.