Question 209247
Two varieties of animal feed contain essential nutrients A and B. 
Feed I contains 2 units of A and 3 units of B per pound. 
Feed II contains 2 units of A and 5 units of B per pound. 
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A farmer needs a feed mix that will give his animals a minimum of 16 units of A and 30 units of B.
"A" Eq.: 2(I)+2(II) >= 16
"B" Eq.: 3(I)+5(II) >= 30
 
If Feed I costs $3 per pound and Feed II costs $4 per pound, how much of each should be bought to supply the proper nutrition while minimizing cost?
Cost Eq: C(x) = 3(I) + 4(II) 
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Write the objective function and system of linear inequalities and solve it graphically using the method of corners.
I >=0
II >=0
"A"Eq: I >= -II+8
"B"Eq: I >= (-5/3)(II) + 10
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{{{graph(400,300,-10,30,-10,30,-x+8,(-5/3)x+10)}}}
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(II,I) Corners:  (0,8), (6,0), (3,5)
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Objective:
C(x) = 3(I) + 4(II)
(0,8) C(x) = 3*8+4*0 = 24
(6,0) C(x) = 3*0+4*6 = 24
(3,5) C(x) = 3*5+4*3 = 27
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Minimal Cost : 8 of I or 6 of II
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Cheers,
Stan H.
Reply to stanbon@comcast.net