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?
:
a = amt of A mix
b = amt B mix
Write an equation for each ingredient and put in the slope/intercept form
:
Phos Acid
20a + 10b = 400
Simplify divide by 10 
b + 2a = 40
b = -2a + 40, red
Nitrogen
30a + 30b = 990
simplify divide by 30
a + b = 33
b = -a + 33, green
Potash
5a + 10b = 210
divide by 10
.5a + b = 21
b = -.5a + 21, blue
;
Plot these three equations
{{{ graph( 300, 200, -20, 50, -20, 50, -2x+40, -x+33, -.5x+21) }}}
two intersections that interest us, a=7, b=26  and   a=24, b=9
Find the cost when a=7, b=26
20(7) + 40(26) = $1180
Find the cost when a=24, b=9
20(24) + 40(9) = $840, this is the obvious choice, A=24 cu/yds, B=9 cu/yds