What do the slope and y-intercept of a real-world linear function represent?
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Let x = the number of spruce trees
Let y = the number of maple trees
The information given is summarized in the following table.
Number Cost/tree Area used CO₂ absorption
----------- ------------- --------------- ----------------------
x $30 600 ft² 650 lb/yr
y $40 900 ft² 300 lb/yr
The amount available to spend is $2100, therefore
30x + 40y ≤ 2100
or
(3/4)x + y ≤ 52.5 (1)
The land available for planting is 45,000 ft², therefore
600x + 900y ≤ 45000
or
(2/3)x + y ≤ 50 (2)
The amount of CO₂ removed per year is
A = 650x + 300y (3)
The shaded area in the graph shown below is the solution region.
Optimum values of A occur at the vertices, as shown.
The maximum removal rate occurs at (70, 3.33) at a rate of 46,500 lb/year.
Because we should have an integral number of trees, we should have
70 spruce and 3 maple trees.
Answer: 70 spruce, 3 maple
Let y = the number of maple trees
The information given is summarized in the following table.
Number Cost/tree Area used CO₂ absorption
----------- ------------- --------------- ----------------------
x $30 600 ft² 650 lb/yr
y $40 900 ft² 300 lb/yr
The amount available to spend is $2100, therefore
30x + 40y ≤ 2100
or
(3/4)x + y ≤ 52.5 (1)
The land available for planting is 45,000 ft², therefore
600x + 900y ≤ 45000
or
(2/3)x + y ≤ 50 (2)
The amount of CO₂ removed per year is
A = 650x + 300y (3)
The shaded area in the graph shown below is the solution region.
Optimum values of A occur at the vertices, as shown.
The maximum removal rate occurs at (70, 3.33) at a rate of 46,500 lb/year.
Because we should have an integral number of trees, we should have
70 spruce and 3 maple trees.
Answer: 70 spruce, 3 maple