Planning crop acreage….(Inequalities and Graph)?
A farmer, in the business of growing fodder for livestock, has 90 acres available for planting alfalfa and corn. The cost of seed per acre is $4 for alfalfa and $6 for corn. The total cost of labor will amount to $20 per acre for alfalfa and $10 per acre for corn. The expected income is $110 per acre from alfalfa and $150 per acre from corn. If the farmer does not wish to spend more than $480 for seed and $1400 for labor, how many acres of each crop should be planted to obtain the maximum profit?
The answer in the back of the book is: None of alfalfa and 80 acres of corn. I need to know how to set up the equation.
Define your variables first.
x=alfalfa, y=corn
Look at what seems to belong together: cost of seed per acre.
4x+6y<_480
Next cost of labor.
20x+10y<_1400
Acres of land.
x+y<_90
Then you need to include x>_0 and y>_0 since you can’t have negative amounts.
Finally, the equation for the maximum profit:
P=110x+150y
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