A farmer have 21 acre land he sowed 3/7 jower 2/7 cotton how many land remain empty
Answers
let x be the acres of wheat planted and
y be the acres of rye planted
Given that there are a total of 10 acres of land to plant.
Atleast 7 acres is to be planted i.e., x+y≥7
Given that the cost to plant one acre of wheat is $200
Therefore, the cost for x acres of wheat is 200x
Given that the cost to plant one acre of rye is $100
Therefore, the cost for y acres of rye is 100y
Given that, an amount for planting wheat and rye is $1200
Therefore the total cost to plant wheat and rye is 200x+100y≤1200⟹2x+y≤12
Given that, the time taken to plant one acre of wheat is 1 hr
Therefore, the time taken to plant x acres of wheat is x hrs
Given that, the time taken to plant one acre of rye is 2 hrs
Therefore, the time taken to plant y acres of rye is 2y hrs
Given that, the total time for planting is 12 hrs
Therefore, the total time to plant wheat and rye is x+2y≤12
Given that, one acre of wheat yields a profit of $500
Therefore, the profit from x acres of wheat is 500x
Given that, one acre of rye yields a profit of $300
Therefore, the profit from y acres of wheat is 300y
therefore the total profit from the wheat and rye is P=500x+300y
In the above figure, the blue shaded region is the feasible region with three corner points.(4,4),(2,5),(5,2)
Now substituting the corner points the profit equation,
substituting (4,4)⟹P=500x+300y=500(4)+300(4)=3200
substituting (2,5)⟹P=500x+300y=500(2)+300(5)=2500
substituting (5,2)⟹P=500x+300y=500(5)+300(2)=3100
$3200 is the maximum profit.
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