1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
rjkz [21]
2 years ago
9

A dairy company gets milk from two dairies and then blends the milk to get the desired amount of butterfat. Milk from dairy I co

sts ​$2.40 per​ gallon, and milk from dairy II costs ​$0.80 per gallon. At most ​$144 is available for purchasing milk. Dairy I can supply at most 50 gallons averaging 3.9​% ​butterfat, and dairy II can supply at most 90 gallons averaging 2.9​% butterfat. Answer parts a and b. a. How much milk from each supplier should the company buy to get at most 100 gallons of milk with the maximum amount of​ butterfat? The company should buy 40 gallons from dairy I and 60 gallons from dairy II. What is the maximum amount of​ butterfat? 330 gallons ​(Type an integer or a​ decimal.) b. The solution from part a leaves both dairy I and dairy II with excess capacity. Calculate the amount of additional milk each dairy could produce. The excess capacity of dairy I is 10 ​gallons, and for dairy II it is 30 gallons. Is there any way all this capacity
Mathematics
1 answer:
zubka84 [21]2 years ago
3 0

Answer:

a) i The company should buy 40 gallons from dairy I and 60 gallons from dairy

ii) What is the maximum amount of​ butterfat? The total amount of butterfat from Diary I and Diary II = 3.12% + 1.93%

=5.05%

b.The excess capacity of dairy I is 10 ​gallons, and for dairy II it is 30 gallons.

Step-by-step explanation:

a. How much milk from each supplier should the company buy to get at most 100 gallons of milk with the maximum amount of​ butterfat?

From the question, we are told that:

Milk from dairy I costs ​$2.40 per​ gallon, Milk from dairy II costs ​$0.80 per gallon.

Let's represent:

Number of gallons of Milk from dairy I = x

Number of gallons of Milk from dairy II = y

At most ​$144 is available for purchasing milk.

$2.40 × x + $0.80 × y = 144

2.40x + 0.80y = 144........ Equation 1

x + y = 100....... Equation 2

x = 100 - y

2.40(100 - y) + 0.80y = 144

240 - 2.4y + 0.80y = 144

-1.60y = 144 - 240

-1.6y = -96

y = -96/-1.6

y = 60

From Equation 2

x + y = 100....... Equation 2

x + 60 = 100

x = 100 - 60

x = 40

Therefore, since number of gallons of Milk from dairy I = x and number of gallons of Milk from dairy II = y

The company should buy 40 gallons from dairy I and 60 gallons from dairy

II. What is the maximum amount of​ butterfat?

From the question

Dairy I can supply at most 50 gallons averaging 3.9​% ​butterfat,

50 gallons = 3.9% butterfat

40 gallons =

Cross Multiply

= 40 × 3.9/50

= 3.12%

Dairy II can supply at most 90 gallons averaging 2.9​% butterfat.

90 gallons of milk = 2.9% butter fat

60 gallons of milk =

Cross Multiply

= 60 × 2.9%/90

=1.9333333333%

≈ 1.93%

The total amount of butterfat from Diary I and Diary II = 3.12% + 1.93%

=5.05%

b. The solution from part a leaves both dairy I and dairy II with excess capacity. Calculate the amount of additional milk each dairy could produce.

Excess capacity of Diary I =

50 gallons - 40 gallons = 10 gallons

Excess capacity of Diary II =

90 gallons - 60 gallons = 30 gallons

Therefore, the excess capacity of dairy I is 10 ​gallons, and for dairy II it is 30 gallons.

You might be interested in
1.Graph the functions on the same coordinate plane.
mel-nik [20]
1. solutions are intersection points
they intersect at x=4 and x=1 or the points (4,0) and (1,0)
select 4 and 1



2.
sub -x for x
if you get the same function, it is even
if you get the exact negative of the function, it is odd
if neither, then neither
basically
f(-x)=f(x) is even
f(-x)=-f(x) is odd
and neither is neighter

so
f(-x)=-2(-x)²+3(-x)
f(-x)=-2(x)²-3x
f(-x)=-2x²-3x
that is not the same function nor is it the exact oposite
neither even nor odd




3.
domain is the time you can use
obvioulsy start at time=0
and stop when it hits the ground because it shouldn't go underground
so domain is all real numbers from 0 to 5 including 0 and 5
that is [0,5]



4. (the (f+g)(x) one)
(f+g)(x)=f(x)+g(x)
so that is just
x²-36+x³+2x²-10=
x³+3x²-46


5. just mulitply them
x⁷+9x⁴-9x³-81

6. minus them
(3x⁵+6x²-5)-(2x⁴+7x²-x+16)
3x⁵+6x²-5-2x⁴-7x²+x-16
3x⁵-2x⁴-x²+x-21
4 0
2 years ago
Jamal ran 7 kilometers, sprinted 400 meters, and climbed bleachers for a distance of 1.6 kilometers during track practice. How m
seraphim [82]
First, convert 7 kilometers to meters, which is 7000 meters.
Add that to 400, and now you he ran 7400 meters.
Now convert 1.6 kilometers to meters, which is 1600 meters.
Add that to 7400, and the total is 9000 meters.

Hope this helped!
4 0
3 years ago
Read 2 more answers
I need the answer fast please find the tan(b)
PSYCHO15rus [73]

Answer:

\sf \dfrac{17}{25}

Step-by-step explanation:

<h3>Trigonometry:</h3>

    \sf \boxed{\bf Tan \ B=\dfrac{oppoiste \ side \ to \ Tan \ B}{hypotenuse}}

         \sf tan \ B =\dfrac{17}{25}

6 0
1 year ago
A grocery store has a shelf with half-gallon containers of milk. What type of number best represents the total number of gallon?
Advocard [28]
Rational numbers.

The grocery store will have a whole number of half gallons =>

number of gallons = n * [1/2] , where n = ∈ N

That means that the number of gallons ∈ Z+ and 0.

Then the answer is the option A. rational number. 
4 0
3 years ago
Jocelyn and her children went into a bakery and she bought $9 worth of cookies and brownies. Each cookie costs $0.50 and each br
Yuliya22 [10]

Jace bought 4 cookies and 2 brownies from the bakery.

Let x represent the number of cookies and y represent the number of brownies.

Since he bought $9 worth of cookies and brownies. Each cookie costs $0.75 and each brownie costs $3. hence:

0.75x + 3y = 9      (1)

Also, he bought twice as many cookies as brownies, hence:

x = 2y

x - 2y = 0     (2)

Solving equation 1 and 2 simultaneously gives x = 4, y = 2

Hence Jace bought 4 cookies and 2 brownies from the bakery.

6 0
2 years ago
Other questions:
  • 15 points!
    14·1 answer
  • Which of the following describes a situation in which the total distance a car travels is 0 meters from its starting point?
    7·2 answers
  • Two lines have the following equations
    11·1 answer
  • To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equati
    9·1 answer
  • (2x + 3y - 4) – (5x + 2)​
    15·1 answer
  • If there is a $50 profit on the large cabinets and a $30 profit on the small cabinets.
    9·1 answer
  • Solve for x... Please i need help!
    12·1 answer
  • Which of the following is an example of a set of like terms? A. 19y, 19, y. B. 18x, -x, 21x. C. 15, 20, 25y. D. -2x, -2y, -2xy.
    10·1 answer
  • Follow the steps to finish solving the equation -3x +18 = 7x
    7·2 answers
  • 2.
    15·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!