A person requires 10, 12 and 12 units of chemicals A, B and C respectively for his garden. A liquid product contains 5, 2 and 1 units of A, B and C respectively per jar. A dry product contains 1, 2 and 4 units of A, B and C per carton. If the liquid product sells for $3 per jar and the dry product sells $2 per carton, how many of each should be purchased in order to minimize cost and meet the requirement?
Answers
Given : A person requires 10, 12 and 12 units of chemicals A, B and C respectively for his garden.
A liquid product contains 5, 2 and 1 units of A, B and C respectively per jar.
A dry product contains 1, 2 and 4 units of A, B and C per carton.
the liquid product sells for $3 per jar and the dry product sells $2 per carton,
To Find : how many of each should be purchased in order to minimize cost and meet the requirement?
Solution:
A ≥ 10
B , C ≥ 12
Let say
Liquid product - x jar and dry product y carton
=> A = 5x + y ≥ 10
B = 2x + 2y ≥ 12 => x + y ≥ 6
C = x + 4y ≥ 12
x , y ≥ 0 as can not be negative
Cost Z = 3x + 2y
Boundary points are
( 0 , 10) , (1 , 5) , ( 4 , 2) and (12 , 0)
Z = 3x + 2y
x = 0 , y = 10 z = 20
x = 1 , y = 5 z = 13
x = 4 , y = 2 z = 16
x = 12 , y = 0 z = 36
Hence minimum cost 13 when x = 1 and y = 5
Liquid product - 1 jar and dry product 5 carton cost 13 $
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