Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Help with linear programming.!?
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 650lb/yr of carbon dioxide and maple trees absorb 300lb/yr of carbon dioxide. How many of each tree should the city plant to maximize carbon dioxide absorption?
1 Answer
- 9 years agoFavorite Answer
first some definitions:
S, M - number of spruce and number of maple trees (decision variables)
Z - target function, total carbon dioxide absorption
c-s = 30, c-m = 40 - cost of spruce and maple trees
a-s = 600, a-m = 900 - required area of spruce and maple trees
o-s = 650, o-m = 300 - CO2 absorption of spruce and maple trees
now for the problem statement and constraints:
max Z = o-s*S + o-m*M
s.t.
c-s*S + c-m*M <= 2,100
a-s*S + a-m*M <= 45,000
You can use any program to solve this (or solve it using simplex). Although in this case, it is a "no brainer". Spruces are cheaper, require less area and absorb more CO2, so you should plant as many Spruces as possible and no Maples at all !
As the saying goes: " it is better to be rich, young and handsome, than poor, old and ugly "
solution:
S = 70, M = 0
budget constraint is active, area constraint isn't
Z = 45,500 - total CO2 absorption
