a farmer has 10 acres total which he can plant in wheat and rye. he has to plant

Question

a farmer has 10 acres total which he can plant in wheat and rye. he has to plant at least 7 acres. however, he has only $1200 to spend and each acre of wheat costs $200 to plant and each acre of rye costs $100 to plant. moreover the farmer has to get the planting done in 12 hours and it takes an hour to plant an acre of wheat and 2 hours to plant an acre of rye. if the profit is $500 per acre of wheat and $300 per acre of rye how many acres of each should be planted to maximize profits? let x be the number of acres of wheat and y be number of acres of rye he plants.
1. write down a two linear inequalities for the number of acres he can plant.
2. write down a linear inequality for the cost to plant the crops.
3. write down a linear inequality for the time to plant the crops.
   there are 2 other linear equations that must be met x>=0 y>=0
4. write down the profit function for the sale of x acres wheat and y acres rye

you now have 5 linear inequalities and a profit function. these together describe the farmers planting situation. these togethere make up what is known as a linear programming problem. write all of the inequalities and the profit function together below.
5. to solve this problem, you will need to graphthe intersection of all the inequalities on one common xy plane. do this on the grid below being careful to draw a straight line and to shade the correct side of each line. let the bottom left be the origin, with the horizontal axis representing x and the vertical axis being y. 6.
you should get a triangular shape where you shaded for all inegqualities. find teh coordinates of the ordcered pairs that make up the vertices of the triangle(the corners). to find these you have the intersection of the 2 lines that make up a corner. solve the 2 by 2 system made up of thier equations. a farmer has 10 acres total which he can plant in wheat and rye. he has to plant at least 7 acres. however, he has only $1200 to spend and each acre of wheat costs $200 to plant and each acre of rye costs $100 to plant. moreover the farmer has to get the planting done in 12 hours and it takes an hour to plant an acre of wheat and 2 hours to plant an acre of rye. if the profit is $500 per acre of wheat and $300 per acre of rye how many acres of each should be planted to maximize profits? let x be the number of acres of wheat and y be number of acres of rye he plants.
1. write down a two linear inequalities for the number of acres he can plant.
2. write down a linear inequality for the cost to plant the crops.
3. write down a linear inequality for the time to plant the crops.
   there are 2 other linear equations that must be met x>=0 y>=0
4. write down the profit function for the sale of x acres wheat and y acres rye

you now have 5 linear inequalities and a profit function. these together describe the farmers planting situation. these togethere make up what is known as a linear programming problem. write all of the inequalities and the profit function together below.
5. to solve this problem, you will need to graphthe intersection of all the inequalities on one common xy plane. do this on the grid below being careful to draw a straight line and to shade the correct side of each line. let the bottom left be the origin, with the horizontal axis representing x and the vertical axis being y. 6.
you should get a triangular shape where you shaded for all inegqualities. find teh coordinates of the ordcered pairs that make up the vertices of the triangle(the corners). to find these you have the intersection of the 2 lines that make up a corner. solve the 2 by 2 system made up of thier equations.

Explanation / Answer

1. x+y is less than or equal to 10 and x+y is greater than or equal to 7 2. 200x+100y is less than or equal to 1200
3. x+2y is less than or equal to 12 4. Profit=500x+300y you would graph these and shade properly (if its less than shade below the line greater than shade above)..when you shade you get a small triangle with three intersection pts which should are
(2,5) & (5,2) & (4,4)
now you plug these points into your profit equation (2,5) Profit=2500 (5,2) Profit=3100 (4,4) Profit= 3200
The point (4,4) gives you the max profit, therefore 4 acres of wheat and 4 acres of rye would give the farmer a max profit

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