A chicken farmer can buy a special food mix A at 20 c per pound and a special food mix B at 40 c per pound. Each pound of mix A contains 3 , 000 units of nutrient N 1 and 1 , 000 units of nutrient N 2 ; each pound of mix B contains 4 , 000 units of nutrient N 1 and 4 , 000 units of nutrient N 2 . If the minimum daily requirements for the chickens collectively are 36 , 000 units of nutrient N 1 and 20 , 000 units of nutrient N 2 , how many pounds of each food mix should be used each day to minimize daily food costs while meeting (or exceeding) the minimum daily nutrient requirements? What is the minimum daily cost? Construct a mathematical model and solve using the geometric method.
A chicken farmer can buy a special food mix A at 20 c per pound and a special food mix B at 40 c per pound. Each pound of mix A contains 3 , 000 units of nutrient N 1 and 1 , 000 units of nutrient N 2 ; each pound of mix B contains 4 , 000 units of nutrient N 1 and 4 , 000 units of nutrient N 2 . If the minimum daily requirements for the chickens collectively are 36 , 000 units of nutrient N 1 and 20 , 000 units of nutrient N 2 , how many pounds of each food mix should be used each day to minimize daily food costs while meeting (or exceeding) the minimum daily nutrient requirements? What is the minimum daily cost? Construct a mathematical model and solve using the geometric method.
Solution Summary: The author calculates the amount of food of mix A and mix B in pounds by geometric method to minimize daily food costs and meet the daily nutrient requirement.
A chicken farmer can buy a special food mix
A
at
20
c
per pound and a special food mix
B
at
40
c
per pound. Each pound of mix
A
contains
3
,
000
units of nutrient
N
1
and
1
,
000
units of nutrient
N
2
; each pound of mix
B
contains
4
,
000
units of nutrient
N
1
and
4
,
000
units of nutrient
N
2
. If the minimum daily requirements for the chickens collectively are
36
,
000
units of nutrient
N
1
and
20
,
000
units of nutrient
N
2
, how many pounds of each food mix should be used each day to minimize daily food costs while meeting (or exceeding) the minimum daily nutrient requirements? What is the minimum daily cost? Construct a mathematical model and solve using the geometric method.
11. Find the composition fog and gof for the following functions.
2
(a) f(x) = 2x+5, g(x) = x²
2
(b) f(x) = x²+x, g(x) = √√x
1
(c) f(x) = -1/2)
9
9(x) =
х
=
-
X
practice problem please help!
13. A restaurant will serve a banquet at a cost of $20 per person for the first 50 people and $15 for person for
each additional person.
(a) Find a function C giving the cost of the banquet depending on the number of people p attending.
(b) How many people can attend the banquet for $2000?
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