A farmer uses two types of fertilizers. A 50lb bag of fertilizer A contains 6 lb of nitrogen and 3lb of phosphorus. A 50 lb bag of fertilizer B contains 4 lb each of nitrogen and phosphorus. The minimum requirements for a field are 480 lb of nitrogen and 240 lb of phosphorus. If a 50lb bag of fertilizer A costs $35 and a 50 lb bag of fertilizer B costs $25 find the amount of each type of fertilizer the farmer should use to minimize his cost while still meeting the minimum requirements. mathematically formulate and state the problem.

Answers

Answer 1

Answer:

Fertilizer A = 20, Fertilizer B = 56

Step-by-step explanation:

Step 1: Set up the equations

Nitrogen: 8x + 5y ≥ 440

Phosphorous: 2x + 5y ≥ 260

Potassium: 4x + 5y ≥ 360

Step 2: Find the vertices

It is easiest to graph the equations to find the vertices. (see attachment).  You can also solve each system of equations to find the intersected points.

The following satisfy the "greater than or equal to" requirement:

(0, 88) → y-intercept of Nitrogen equation

(20, 56) → intersection of Nitrogen and Potassium equations

(50, 32) → intersection of Phosphorous and Potassium

(130, 0) → x-intercept of Potassium

Step 3: Use vertices in cost function C(x) to find the minimum

C(x) = $30x + $20y

(0, 88): $30(0) + $20(88) = $1760

(20, 56): $30(20) + $20(56) = $1720    ← This is the minimum!

(50, 32): $30(50) + $20(32) = $2140

(130, 0): $30(130) + $20(0) = $3900

The minimum cost occurs when 20 bags of Fertilizer A and 56 bags of Fertilizer B are purchased.  


Related Questions

Explain how you can multiply to find equivalent fractions

Answers

Answer:

One example for an equivalent fraction would be 2/5 = 4/10

Step-by-step explanation:

It is equivalent because in both the denominator and the numerator you multiply by 2 which means that if you would divide 4/10 by 2 top and bottom, you would get 2/5. If you were to but these fractions on a number line; one on top of the other; they would equally have one under the other.

*** I hope this helps (brainly if possible)

Help me with questions please​

Answers

2290.22mm^2
Hope this helped

Anna adds 2oz of milk to an 18oz cup of coffee that is 10% milk. What is the percentage of the milk in the resulting mixture?

Answers

Answer:

19% of milk

lemme know if it helped

Step-by-step explanation:

Find the slope given these points:
(4,-4) & (2,0)

Answers

Answer:

The slope is -2

Step-by-step explanation:

[tex]m = \frac{0 - ( - 4)}{2 - 4 } \\ m = \frac{4}{ - 2 } \\ m = - 2[/tex]

Answer:

this is correct

Explanation

signs

1 quadrant = (+,+)

2 quadrant = (-,+)

3 quadrant = (-,-)

4 quadrant = (+,-)

If it takes you 2 1/2 hours to assemble one unit, how many units will you complete in 15 hours? (Change 2 1/2 to improper fraction first)

Answers

Answer:37.5

Step-by-step explanation:

2 1/2 as an improper fraction is 5/2

If i'm wrong tell me please i hope this helped you

Lines r and s are perpendicular and intersect at point k ray kt is drawn forming angles 1 and 2 if angle 1 is 4x-12 and angle 2 equals 3x -8 what is angle 1 to nearest 10th

Answers

The measure of angle 1 to the nearest tenth is 50.9 degrees

Since the line r and s are perpendicular, hence the sum of the angle m<RKT and m<SKT is 90 degrees.

Given the following parameters

m<RKT  = m<1 = 4x - 12

m<SKT = m<2 = 3x - 8

Taking the sum of the angle and equating it to 90degrees, hence;

m<RKT  +m<SKT = 90

4x - 12 + 3x - 8 = 90

7x = 90 + 20

7x = 110

x = 110/7

x = 15.71

Get the measure of angle 1

m<1 = 4x - 12

m<1 = 4(15.71) - 12

m<1 = 50.9 degrees

Hence the measure of angle 1 to the nearest tenth is 50.9 degrees

Learn more here: https://brainly.com/question/11828005

The angle measure of a triangle is shown in the diagram.
what is the value of x?
A. 13
B. 20
C. 5
D. 12

Answers

Answer:C.5

Step-by-step explanation:

See attachment picture please

Answers

Answer:

How can we answer it without question?

Which statement is true?

Answers

The answer is a
Hope this helped!!

Hey whats 2+2? i need to know ASAP! IM IN PRESCHOOL-

Answers

Answer:

lol Its 4

Step-by-step explanation:

Dont worry you got this

Answer:

=4

Step-by-step explanation:

2 + 2 = 4

1 + 1 = 2

1 + 3= 4

Hope this helps, have a nice day/night! :D

if it helps, please mark as brainliest!

trevin puts 8 gallons of

Answers

Answer:

24.75 is answer

Step-by-step explanation:

Answer:

That was a good start, but we need the rest of the question.

Step-by-step explanation:

4 A neghborhood is debating whether or not to have a leash law, which would require all dogs outside of homes to be on a leash. Most of the dog owners live in the
northern part of the
neghborhood. Which of these polls should give the most accurate information?
O A Apoll in which two streets are chosen at random and all the houses are on those two streets are polled.
OB. A poll in which the northernmost street and the southernmost street are both polled
• C. A poll in which 50 people in the neighborhood are chosen by picking addresses out of a hat.
OD. A poll in which 25 people are chosen by picking random phone numbers.

Someone please help
Will give brainliest

Answers

Answer:

C. A poll in which 50 people in the neighborhood are chosen by picking addresses out of a hat.

Step-by-step explanation:

It limits the field to those the law would affect, yet is randomized within that field to not bias the results much.

Find the nth term of the geometric sequence.

Answers

[tex]a_2 = ar^{2-1} =ar = 6~~ ...(i)\\\\a_4 = ar^{4-1} = ar^3 = 2186 ~~....(ii)\\\\\\(ii)\div (i):\\\\\dfrac{ar^3}{ar} = \dfrac{2186}6\\\\\implies r^2 = \dfrac{2186}6 = \dfrac{1093}3\\\\\implies r = \pm \sqrt{\dfrac{1093}3}\\\\a= \pm \dfrac{6}{ \sqrt{\dfrac{1093}3}}\\\\\text{nth term} = ar^{n-1} = \pm \dfrac{6}{ \sqrt{\dfrac{1093}3}} \left( \pm{ \sqrt{\dfrac{1093}3} \right)^{n-1} = \dfrac{6}{ \sqrt{\dfrac{1093}3}} \left( { \sqrt{\dfrac{1093}3} \right)^{n-1} \\\\\\[/tex]

[tex]= 6\left(\dfrac{1093}3 \right)^{\tfrac{n-2}2}[/tex]

Answer:

aₙ = (6/19)*19ⁿ⁻¹

Step-by-step explanation:

Given:

a₂ = 6a₄ = 2166

Equation of nth term of GP:

aₙ = a₁rⁿ⁻¹

Substitute for 2nd and 4th terms:

a₂ = a₁r = 6a₄ = a₁r³ = 2166

Substitute the value of a₂ into a₄ and find the value of r:

a₁r³ = a₁r * r² = 6r²6r² = 2166r² = 2166/6r² = 361r = √361r = 19

Find the first term:

a₁r = 6a₁*19 = 6a₁ = 6/19

The equation of nth term is:

aₙ = (6/19)*19ⁿ⁻¹

Which one is the correct answer ? Find the amplitude , period. Phase shift asymptotes domain range Use the fact that cos(x)=0 will be an asymptote

Answers

Answer:

3. is your correct answer ok

Is the following a reflection,
rotation or translation?

Answers

This is a translation

Have a good day and remember to smile!

Answers

AWW you to have a good day!

0.98x0.23 what is 0.98 times 0.23?

Answers

Answer:

0.2254

Step-by-step explanation:

multiply using long multuplication

I need help solve the equation

Answers

Answer:

  y = x +1

Step-by-step explanation:

The line meets the y-axis (on the left side of the graph) at y=1. This is the y-intercept (b).

The line goes up 1 grid square for each 1 grid square to the right. Its slope is ...

  m = rise/run = 1/1 = 1

Now, we know m and b so we can write the slope-intercept equation for the line:

  y = mx +b . . . . . . line with slope m and y-intercept b

  y = x +1

PLEASE HELP!! REWARDING LOTS OF POINTS!

Answers

Step-by-step explanation:

check the attached file

helppppppppppppppppppppppppppp
A machine cuts a strip of carpet into two pieces. The length of the smaller piece is 5 meters greater than 1/4 the length of the larger piece. If the length of the smaller piece is 12 meters, the length of the bigger piece is _____________ meters
and the total length of the carpet is _____________ meters.

Answers

Answer:

longer = 28 meters

Total = 40 meters

Step-by-step explanation:

Let the smaller piece be s,

and the longer piece be b

s = ¼b + 5

s = 12

¼b + 5 = 12

¼b = 7

b = 28 m

Total length = 28+12 = 40 meters

Which of the following is a solution to the given equation?
y=-3x - 7
A)
(-2,-1)
B)
(-1,-10)
C
(4,-5)
D
(3,-2)

Answers

Answer: A

Step-by-step explanation:

By replacing in the given equation:

y=-3x-7

y=-3(-2)-7

y=6-7

y=-1

But for choices B, C and D the given x values don't fit with the images.

Calculator
Which ordered pair is the solution to the system of equations?
1 -5x - 3y = 12
Y=x-12
0 (0, -4)
0 (-6, 6)
O (1, -11)
O (3,-9)

Answers

[tex] \text{Given : Which ordered pair is the solution to the system of equations?} \\ \\ \begin{cases}-5x - 3y = 12 \\ y - x = 12 \end{cases} [/tex]

[tex] \text{Solution : According to the question, here let's take these variables as two} \\ \text{equations then get their value and finally get the answer.} \\ \\ \sf {1}^{st} \: equation : \\ \leadsto \frak{-5x - 3y = 12} \\ \\ \leadsto \frak{-5x = 12 + 3y} \\ \\ \leadsto \frak{x= \frac{12 + 3y}{-5}} \qquad \sf ...eq(1) \\ \\ \sf 2^{nd} \: equation : \\ \leadsto \frak{y = x - 12} \qquad \sf ...eq(2) \\ \\ \underline{ \frak{finding \: x }} : \\ \\ \dashrightarrow \frak{x= \frac{12 + 3y}{-5}} \\ \\ \dashrightarrow \frak{x= \frac{12 + 3(x - 12)}{-5}} \\ \\ \dashrightarrow \frak{x= \frac{12 + 3x - 36}{-5}} \\ \\ \dashrightarrow \frak{-5x= 12 + 3x - 36} \\ \\ \dashrightarrow \frak{-5x - 3x= - 24} \\ \\ \dashrightarrow \frak{-8x = - 24} \\ \\ \star \quad \underline{ \boxed{ \green{ \frak{x = 3}}}} \\ \\ \underline{ \frak{ getting \: y}} : \\ \\ \dashrightarrow \frak{y = 3 - 12} \\ \\ \star \quad\underline{ \boxed{\blue{ \frak{y = - 9}}}} \\ \\ [/tex]

[tex] \green{ \mathbb{HENCEFORTH, \: THE \: PAIR \: IS \: \pink{\frak{ (3,-9)}}}}[/tex]

In a simple random sample of 120 women and 150 men from
a population of 150,000, 25% of the women and 37% of the men
are smokers. Suppose you are interested in comparing the
proportion of smokers by sex, compute the estimated standard
error.

Answers

From the information given, and applying the formula, it is found that the standard error of the difference in proportion of smokers by sex is 0.0558.

The proportion and the standard error for each sample are given by:

[tex]p_W = 0.25, s_W = \sqrt{\frac{0.25(0.75)}{120}} = 0.0395[/tex]

[tex]p_M = 0.37, s_M = \sqrt{\frac{0.37(0.63)}{150}} = 0.0394[/tex]

The standard error of the difference in proportions is the square root of the sum of the standard error for each sample squared, hence:

[tex]s = \sqrt{s_W^2 + s_M^2} = \sqrt{0.0395^2 + 0.0394^2} = 0.0558[/tex]

Hence, the standard error is of 0.0558.

A similar problem is given at https://brainly.com/question/25649070

Scientific notation question in mathematics please answer
A newly discovered planet has a mass of 4.8743 · 10 22 kilograms. It's estimated that there is water on the surface and that, the water's mass is only 4 · 10 -2 percent of the planet's total mass. Use scientific notation to estimate the mass of the planet's water. In your final answer, include all of your estimates and calculations.

Answers

Answer:

1.94972 × 10¹⁹ kg

Step-by-step explanation:

Mass of the planet:

4.8743 × 10²² kg

The water's mass:

4×10⁺²%

Mass of the planet's water:

4.8743 × 10²² * 4×10⁺² / 100 = 19.4972 × 10²²⁺²⁺² = 19.4972 × 10¹⁸ = 1.94972 × 10¹⁹

Natalie and her sister opened a savings account at the same time. Natalie deposited $100 and will deposit $10 each month. Her sister deposited $25 and will deposit $25 each month. When will Natalie have less money in her account that her sister?

Answers

Answer:

6 months

Step-by-step explanation:

We can think of Natalie as 100 + 10x and her sister as 25 + 25x. If we put them together, we will get 100 + 10x < 25 + 25x, We can simplify it by moving the 25 to the left side and 10x to the right side. Then we will get 75 < 15x, and the smallest solution is 6 because 5 * 15 is equal to 75

PLEASE ANSWER ASAP (no links please)
Solve for the indicated variable


g/h = e - 10 for g

Answers

Answer:

g = he - 10h

Step-by-step explanation:

Work out Simplify if possible.

Answers

Answer:

a.1×9/1=9

b.3×5/1=15 i think this would be the answer

Answer:

a) 9

b) 15

you

can

download

photo

math

to help you with your math :)

Hope this helps you......

9:12=15:______

I need the answer pls!

Answers

Answer:

15:20

Step-by-step explanation:

We can simplify the ratio to 3:4

after doing that we can multiply both sides by 5 giving us

                          15:20   as our answer

Or you can cross multiply

9 : 12 = 15 : x

Now we have 9x = 180

divide both sides by 9 and we get

x=20

which would work giving us the ratio of                         9 : 12 = 15 : 20

which function is represented by the graph?

Answers

Answer:

[tex]y=-\sqrt{x+2}-1[/tex]

Step-by-step explanation:

Hi there!

Please take a look at the attached image. This is the parent function of the radical function.

[tex]y=\sqrt{x}[/tex]

This equation represents the transformations of the parent function:

[tex]y=a\sqrt{b(x-h)}+k[/tex]

a dictates vertical stretch.

b dictates horizontal stretch.

h dictates horizontal translation.

k dictates vertical translation.

If we take a look at the given graph, we can tell that the following transformations have been applied:

- reflection across x-axis (a = -1)

- translation 2 units to the left (h = -2)

- translation 1 unit down (k = -1)

Therefore, the function that represents the graph is:

[tex]y=-\sqrt{x+2}-1[/tex]

I hope this helps!

Solve for the missing variable thank you!

Answers

The answer is 58 degrees
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