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?
Accepted Solution
A:
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.