Misha and Dontavious were asked to solve the following problem using linear programming.
A local school district can operate a large bus for $300 per day and a small bus for $200 per day. The district needs to arrange transportation for at least 360 students for a field trip and has enough chaperones to have one chaperone per bus for up to 7 buses. Each large bus can hold 60 students and each small bus can hold 45 students. What is the minimum cost for the transportation for the field trip?

Misha decided the following represented this situation:

Let x = number of large buses

Let y = number of small buses

Objective Fx: C=300x+45y

Constraints:

200+60y≥360

x+y≤7

x≥0

y≥0

Dontavious decided the following represented this situation:

Let x = number of large buses

Let y = number of small buses

Objective Fx: C=300x+200y

Constraints:

60x+45y≥360

x+y≤7

x≥0

y≥0



Decide which student set up the correct Objective function and Constraints and using that information answer the following:

a) What are the vertices for the correct feasible region?

b) What is the minimum cost for transportation for the field trip and how did you arrive at this cost?

Answers

Answer 1

The correct function was: Dontavious

The constraints are the number of students at least 360 and the number of buses up to 7.  

Dontavious wrote  the appropriate inequalities. cost is $300 for large buses and $200 for small buses. and the constraints are the number of students per bus.

a) The feasible region is where the solution spaces overlap: this creates a small triangular area with the vertices at (6, 0), (7, 0) and (3, 4).

(6, 0), (7, 0), (3, 4)

b) 3 large buses and  4 small buses would cost 3*300 + 4*200 = $1700  

6 large buses and  0 small buses would cost 6*300 = $1800 dollars

The cheapest solution would be  3 large buses and 4 small buses which would cost $1700

 

 


Related Questions

Judith has x math problems to do for homework. Harry has 2 times as many problems to do as Judith. Janessa has 10 more math problems to do than Judith. Which expression represents the total number of math problems Judith, Harry, and Janessa have to do all together

Answers

Answer:

4x+10

Step-by-step explanation:

Judith= x

Harry = 2x

Janessa= x+10

expression in total= x+2x+x+10 = 4x+10

Judith: x
Harry: 2x
Janessa: x + 10

x + 2x + x + 10
= 4x + 10

You randomly draw twice from this deck of cards
What is the probability of drawing a 3, then drawing an even number without replacing the first card?

Answers

Answer:

probability: 1/10 or 10%

A is the point (2, 3) and B is the point (7,-5).
Find the co-ordinates of the midpoint of AB.

Answers

Midpoint formula is
X1+x2/2 and y1+y2/2
Plug into
2+7/2
3+-5/2
Midpoint =(4.5 or 9/2 for x, and -1 for y)
(4.5,-1)

Here we would be using the midpoint formula to find the co-ordinates of the line segment joining the two given points.

Given points,

(2 , 3) and (7 , -5)

We have :

x₁ = 2x₂ = 7y₁ = 3y₂ = -5

[tex] \red\bigstar[/tex]Midpoint of two points:-

[tex]\boxed{ \sf{M \: = \: \dfrac{x_1 \: + \: x_2 }{2} \: , \: \dfrac{y_1 \: + \: y_2 }{2}}} \: \pink\bigstar[/tex]

Now, refer to the attachment.

Learn more from brainly :

https://brainly.com/question/23658067https://brainly.com/question/27354466https://brainly.com/question/27354479https://brainly.com/question/27354524https://brainly.com/question/27354542

Find the volume of the cone. Round your answer to the nearest tenth
height is 22 meters and the radius is 11 meters

Answers

2787.64 is the volume..

Two investments totaling $15,500 produce an annual income of $1450. One investment yields 10% per year, while the other yields 5% per year. How much is invested at each rate?

Answers

Answer:10% rate:

Principal = p

Rate = 0.10

Interest = 0.10p

5% rate:

Principal = 15500 - p

Rate = 0.05

Interest = 0.05(15500 - p) = 775 - 0.05p

0.10p + (775 - 0.05p) = 1450

0.05p + 775 = 1450

0.05p = 675

p = 13500

10% rate:

Principal = p = $13,500

5% rate:

Principal = 15500 - p = 15500 - 13500 = $2000

Step-by-step explanation:

hope it helps

can you break it down for me.​

Answers

Answer:

m + 8 ≥ -8

Step-by-step explanation:

1st choice: WRONG

m + 8 ≤ -8

-3 + 8 ≤ -8

5 ≤ -8

2nd choice: WRONG

-m + 8 ≤ -8

-(-3) + 8 ≤ -8

11 ≤ -8

3rd choice: RIGHT

m + 8 ≥ -8

-3 + 8 ≥ -8

5 ≥ -8

4th choice: WRONG

-m + 8 ≤ -8

-(-3) + 8 ≤ -8

11 ≤ -8

Write an equation of the line with the given slope and y-intercept:
m = -5,6 = 4
a. y = -5x + 4
b. y = 5x + 4
c. y = -5x-4
d. y = 5x - 4
Please select the best answer from the choices provided
Ο Ο Ο Ο
D

Answers

Answer:

a. y = -5x + 4

Step-by-step explanation:

Given the following data;

Slope, m = -5

Intercept, c = 4

Mathematically, the equation of line is given by the formula; y = mx + c

Where;

m is the slope.

x and y are the points

c is the intercept.

Substituting the given parameters, we have;

y = -5x + 4

Which equation best describes the graph?
8
2
-8
-6
-4
-2
2
2
8
-2
4
-6
-8
С
A y = 2x + 4
y = -2x +
Dy=-3x+4
B
y = 3x + 4

Answers

Answer:

b  i think    

Step-by-step explanation:

Answer:

b...................

Help me pleaseeee i need to finish

Answers

x = 4
hope all goes well in life :)
have a great day/night/afternoon

Answer:

x=4

Step-by-step explanation:

trust me I got it right

Help? I will give brainlist ! also I report people who add links :) have a good day!

Answers

First one is <
Second is <
Third is =
Fourthly is >

Answer:

1/2 < 3/4,

6/12 < 5/8,

2/3 = 4/6,

3/8 > 1/4

Step-by-step explanation:

Plz mark as Brainllest

Hunter has 6 cups of yogurt to make smoothies. Each smoothie uses 1/2 cup of yogurt.
How many smoothies can Hunter make with the yogurt?

Answers

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

Answer: 12

Explanation:

6 / 1/2 = 6 x 2 = 12

I hope this helped!

<!> Brainliest is appreciated! <!>

- Zack Slocum

*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆*――*☆**☆*――*☆*――*☆*――*☆

PALEEZE Help Me!! The ceiling of Katie’s living room is a square that is 16 ft long on each side. To decorate for a party, she plans to hang crepe paper around the perimeter of the ceiling and then from each corner to the opposite corner. Katie can buy rolls that each contain 28 ft of crepe paper. What is the minimum number of rolls she should buy? Show your work and draw a diagram to support your answer.

Answers

Answer:

At least 4

Step-by-step explanation:

Photo of my work and where I got the equation from

You are conducting a significance test of H0: μ = 5 against Ha: μ > 5. After checking the conditions are met from a simple random sample of 30 observations, you obtain t = 2.35. Based on this result, describe the p-value.

The p-value falls between 0.15 and 0.2.
The p-value falls between 0.025 and 0.05.
The p-value falls between 0.01 and 0.02.
The p-value falls between 0.005 and 0.01.
The p-value is less than 0.005.

Answers

Answer:

The p-value falls between 0.005 and 0.01.

Step-by-step explanation:

Random sample of 30 observations, you obtain t = 2.35

This means that the pvalue is 1 subtracted by the pvalue of Z = 2.35, as we are testing that the mean is more than a value.

Looking at the z-table, z = 2.35 has a pvalue of 0.9906

1 - 0.9906 = 0.0094

So, between 0.005 and 0.01.

Answer: The p-value falls between 0.01 and 0.02.

Step-by-step explanation: I took the FLVS test.

Katie needs 3/4 cup of sugar to make cookies. She only has 1/3 cup. How much more sugar does Katie need?​

Answers

Answer:

[tex]\frac{5}{12}[/tex] cups

Step-by-step explanation:

This question is asking for the difference between the two values so subtraction is necessary

[tex]\frac{3}{4} -\frac{1}{3}[/tex]

Multiply the top and bottom of the first fraction by 3 and the second one by 4[tex]\frac{3*3}{4*3} -\frac{1*4}{3*4} = \frac{9}{12} -\frac{4}{12}[/tex]

Now just substract

9 - 4 = 5  ==>  [tex]\frac{9}{12} -\frac{4}{12} = \frac{5}{12}[/tex]

Which is bigger: 3 pints or 8 cups?

Answers

Answer:

8 cups is bigger

Step-by-step explanation:

3 pints = 6 cups

6 < 8

To find the value of the following expression, which task should be completed first?

Answers

Answer:

subtract inside the parentheses

Step-by-step explanation:

According to pemdas. It is parenthesis first so you subtr what’s inside first

Answer:

Subtract inside the parenthesis

Step-by-step explanation:

For this problems you have to follow PEMDAS which stand for

Parenthesis

Exponents

Multiplication

Division

Addition

Subtraction

in that order

Complete the equation of the line through (1,4) and (2,2)

Use exact numbers.
y=?

Answers

Step-by-step explanation:

slope = 2-4/2-1 = -2

y - 2 = -2(x - 2)

y-2 = -2x +4

y = -2x + 6

Answer:

y = -2x + 6

Step-by-step explanation:

(y-4)/(2-4) = (x-1)/(2-1)

(y-4)/(-2) = x-1

y-4 = -2x +2

y = -2x + 6

QUESTION
The first four terms of a quadratic sequence are 8; 11; 16; 23; .-
Write down the next two terms of the quadratic sequence.
J. 2 Calculate the nth of the quadratic sequence.
i: 5.3 Determine the position of the term 2311 in the sequence.
(1)
(4)
(3)
[8]​

Answers

Answer:

b

Step-by-step explanation:

i need help [lzzzzzzzzzzzzzzzzz

Answers

Lol ok you good buddy?

Help ill Mark brainlist :)

Answers

Answer:

The area would be 40.5 cm ^2

Step-by-step explanation:

Well first you don’t gotta worry about some isosceles trapezoid thingy.

You just gotta know the formula for a trapezoid is (b1+b2)/2)h

B1 in this case is or base 1 (9 or 4.5)

b2 in this case is or base 2 (9 or 4.5)

(you can only choose one base for each)

ANd you add those 2 up and you’d get 13.5

13.5/2 which is 6.75

Now we multiply it by the height which is 6 and gte 40.5

40.5cm ^2 is the final answer

During an economic downturn, 11 companies were sampled and asked whether they were planning to increase their workforce. Only 2 of the 11 companies were planning to increase their workforce. Use the small-sample method to construct an 80% confidence interval for the proportion of companies that are planning to increase their workforce. Round the answers to at least three decimal places.

An 80% confidence interval for the proportion of companies that are planning to increase their workforce is _______ < p< ________

Answers

Answer:

An 80% confidence interval for the proportion of companies that are planning to increase their workforce is 0.033 < p < 0.331.

Step-by-step explanation:

In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.

[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]

In which

z is the zscore that has a pvalue of [tex]1 - \frac{\alpha}{2}[/tex].

Only 2 of the 11 companies were planning to increase their workforce

This means that [tex]n = 11, \pi = \frac{2}{11} = 0.182[/tex]

80% confidence level

So [tex]\alpha = 0.2[/tex], z is the value of Z that has a pvalue of [tex]1 - \frac{0.2}{2} = 0.9[/tex], so [tex]Z = 1.28[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.182 - 1.28\sqrt{\frac{0.182*0.818}{11}} = 0.033[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.182 + 1.28\sqrt{\frac{0.182*0.818}{11}} = 0.331[/tex]

An 80% confidence interval for the proportion of companies that are planning to increase their workforce is 0.033 < p < 0.331.

what is 1086.3961 rounded to the nearest square foot?

Answers

I believe the answer would be 1086.4

Please give a like if I’m right and tell me in the comments if I’m wrong.
Hope this helped :)

Page No
Date:
Convert (1020)5 to base ten numeral

Answers

The answer is 204. Your well

Please help quickly what's the answer Ill give u brainlest
Richard deposits $193.67 every month into his mortgage. At the end of 30 years, he has a balance of $120,182.07. What interest has accrued (been earned) over 30 years?

Answers

193.67 x 12= 2316
1 year=$2316
2316 x 30years= 69,480
120,182.07 -69,480=50,702.07

Please help me i cannot understand these Questions

Answers

Answer:

In the last task, the result is 17+3x/6

Step-by-step explanation:

X+5/3 - 2x-7/6 + x/2

2(x+5)-(2x-7)+3x /6

2x+10-2x+7+3x /6

17+3x/6

I dunno this task above, I hope this one is correct :))

Which equation has a solution of k = 3.5?

Answers

Answer:

an example of an equation?

if you want one step you can try

10k=35

if you want two step

10k-17=18

Step-by-step explanation:

help me with this plzzz

Answers

Answer:

b is the answer

Step-by-step explanation:

if you look at the graph chart you will notice that b lines up with negative 4 and positive 2

Solve the difference of 9x and 8x is 107

Answers

Answer:

x = 107

Step-by-step explanation:

If x = 107,

(9 x 107) - (8 x 107) = 107

Then x must be 107.

Can someone help meeee plz and no link plz is due in 9 minutes

Answers

Answer:

A (4,3)

Step-by-step explanation:

J is inside the parallelogram.

K is indside a trapezium.

So we want to find the coordinates of point J.

Reading from the scales, point J is x = 4 and y = 3.

Writing our answer in the form (x, y) coordinates of J are: (4,3)


Find the area of the trapezoid. Round your answer to the nearest hundredth.

Answers

Answer:

42.50 units²

Step-by-step explanation:

Area of the trapezoid = ½(AB + DC)×AD

AB = 6

DC = 11

AD = ?

Use trigonometric function, TOA to find AD:

Tan 45 = Opp/Adj

Opp = AD

Adj = 11 - 6 = 5

Tan 45 = AD/5

5 × tan 45 = AD

AD = 5

✔️Find Area of trapezoid.

Area = ½(AB + DC)×AD

= ½(11 + 6)×5

= 42.50 units²

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