document.write( "Question 1129285: A farmer can buy two types of plant​ food, mix A and mix B. Each cubic yard of mix A contains 20 pounds of phosphoric​ acid, 30 pounds of​ nitrogen, and 5 pounds of potash. Each cubic yard of mix B contains 10 pounds of phosphoric​ acid, 30 pounds of​ nitrogen, and 10 pounds of potash. The minimum monthly requirements are 400 pounds of phosphoric​ acid, 990 pounds of​ nitrogen, and 210 pounds of potash. If mix A costs ​$20 per cubic yard and mix B costs ​$40 per cubic​ yard, how many cubic yards of each mix should the farmer blend to meet the minimum monthly requirements at a minimum​ cost? What is this​ cost?
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Algebra.Com's Answer #745866 by ankor@dixie-net.com(22740)\"\" \"About 
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A farmer can buy two types of plant​ food, mix A and mix B.
\n" ); document.write( " Each cubic yard of mix A contains 20 pounds of phosphoric​ acid, 30 pounds of​ nitrogen, and 5 pounds of potash.
\n" ); document.write( " Each cubic yard of mix B contains 10 pounds of phosphoric​ acid, 30 pounds of​ nitrogen, and 10 pounds of potash.
\n" ); document.write( " The minimum monthly requirements are 400 pounds of phosphoric​ acid, 990 pounds of​ nitrogen, and 210 pounds of potash.
\n" ); document.write( " If mix A costs ​$20 per cubic yard and mix B costs ​$40 per cubic​ yard, how many cubic yards of each mix should the farmer blend to meet the minimum monthly requirements at a minimum​ cost
\n" ); document.write( "? What is this​ cost?
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\n" ); document.write( "a = amt of A mix
\n" ); document.write( "b = amt B mix
\n" ); document.write( "Write an equation for each ingredient and put in the slope/intercept form
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\n" ); document.write( "Phos Acid
\n" ); document.write( "20a + 10b = 400
\n" ); document.write( "Simplify divide by 10
\n" ); document.write( "b + 2a = 40
\n" ); document.write( "b = -2a + 40, red
\n" ); document.write( "Nitrogen
\n" ); document.write( "30a + 30b = 990
\n" ); document.write( "simplify divide by 30
\n" ); document.write( "a + b = 33
\n" ); document.write( "b = -a + 33, green
\n" ); document.write( "Potash
\n" ); document.write( "5a + 10b = 210
\n" ); document.write( "divide by 10
\n" ); document.write( ".5a + b = 21
\n" ); document.write( "b = -.5a + 21, blue
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\n" ); document.write( "Plot these three equations
\n" ); document.write( "\"+graph%28+300%2C+200%2C+-20%2C+50%2C+-20%2C+50%2C+-2x%2B40%2C+-x%2B33%2C+-.5x%2B21%29+\"
\n" ); document.write( "two intersections that interest us, a=7, b=26 and a=24, b=9
\n" ); document.write( "Find the cost when a=7, b=26
\n" ); document.write( "20(7) + 40(26) = $1180
\n" ); document.write( "Find the cost when a=24, b=9
\n" ); document.write( "20(24) + 40(9) = $840, this is the obvious choice, A=24 cu/yds, B=9 cu/yds\r
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