SOLUTION: help! Nutts nuts has 75lbs of chashew and 120lbs of peanuts. These are to be mixed in 1 pound packages as follows:a low grade mixture that contains 4ounces of cashew and 12ounces

Question 63599: help!
Nutts nuts has 75lbs of chashew and 120lbs of peanuts. These are to be mixed in 1 pound packages as follows:a low grade mixture that contains 4ounces of cashew and 12ounces of peanuts. High grade mixture contains 8 ounces of cashew and 8 ounces of peanuts. On the low-grade mixture a profit of $0.25 a package is to be made while the high-grade mixture profit is to be $0.45 a package. How many packges of each mixture should be made to botain a maximum profit?
x=# of packages of low grade mixture
y=# of package of high grade mixture
The profit P is given by the linear equation
p=($0.25)x + ($0.45)y
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Nutts nuts has 75lbs of chashew and 120lbs of peanuts. These are to be mixed in 1 pound packages as follows:a low grade mixture that contains 4ounces of cashew and 12ounces of peanuts. High grade mixture contains 8 ounces of cashew and 8 ounces of peanuts. On the low-grade mixture a profit of $0.25 a package is to be made while the high-grade mixture profit is to be $0.45 a package. How many packges of each mixture should be made to botain a maximum profit?
x=# of packages of low grade mixture
y=# of package of high grade mixture
The profit P is given by the linear equation
p=($0.25)x + ($0.45)y
Nutts nuts has 75lbs of chashew and 120lbs of peanuts. These are to be mixed in 1 pound packages as follows:a low grade mixture that contains 4ounces of cashew and 12ounces of peanuts. High grade mixture contains 8 ounces of cashew and 8 ounces of peanuts. On the low-grade mixture a profit of $0.25 a package is to be made while the high-grade mixture profit is to be $0.45 a package. How many packges of each mixture should be made to botain a maximum profit?
x=# of packages of low grade mixture
y=# of package of high grade mixture
The profit P is given by the linear equation
p=($0.25)x + ($0.45)y
Nutts nuts has 75lbs of chashew and 120lbs of peanuts. These are to be mixed in 1 pound packages as follows:a low grade mixture that contains 4ounces of cashew and 12ounces of peanuts. High grade mixture contains 8 ounces of cashew and 8 ounces of peanuts. On the low-grade mixture a profit of $0.25 a package is to be made while the high-grade mixture profit is to be $0.45 a package. How many packges of each mixture should be made to botain a maximum profit?
x=# of packages of low grade mixture
y=# of package of high grade mixture
The profit P is given by the linear equation
p=($0.25)x + ($0.45)y
========================
Chashew equation:
(4/16)x+(8/16)y=75
4x+8y=1200
x+2y=300
y=(-1/2)x+150
-----------------
Peanut equation:
(12x/16)+(8y/16)=120
12x+8y=1920
3x+2y=480
y=(-3/2)x+240
----------------
Find the intersection of the Cashew and the Peanut equations.
(-1/2)x+120=(-3/2)x+240
x=120
Solve for y.
y=(-1/2)x+150
y=(-1/2)(120)+150
y=90
-----------------
Check the Profit equation for its maximum at (0,150)(0,240)(120,90)
At (0,240): Profit = 0.25(0)+0.45(240)=$108.00
At (120,90): Profit = 0.25(120)+0.45(90)=$70.50
-----------
Conclusion: Skip production of the low grade; make 240 of the high grade pks.
Cheers,
Stan H.

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