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Maurinko [17]
3 years ago
11

A bus company has contracted with a local high school to carry 450 students on a field trip. The company has 18 large buses whic

h can carry up to 30 students and 19 small buses which can carry up to 15 students. There are only 20 drivers available on the day of the field trip.
The total cost of operating one large bus is $225 a day, and the total cost of operating one small bus is $100 per day.
​
Mathematics
1 answer:
Galina-37 [17]3 years ago
3 0

Answer:

The answer is below

Step-by-step explanation:

Let x represent the big buses and y represent small buses. The large buses can carry 30 students and the small buses can carry 15 students. The total number of students are 450, this can be represented by the inequality:

30x + 15y ≤ 450

They are only 20 drivers, therefore only 20 buses can be used. It is represented by:

x + y ≤ 20

They  are only 19 small buses and 18 large buses:

x ≤ 18

y ≤ 19

After plotting the graph, the minimum solution to the graph are at:

A (15,0), B(18,0), C(10, 10), D(18, 2).

The cost function is given as:

The total cost of operating one large bus is $225 a day, and the total cost of operating one small bus is $100 per day.

​

F(x, y) = 225x + 100y

At point A:

F(x, y) = 225(15) + 100(0) = $3375

At point B:

F(x, y) = 225(18) + 100(0) = $4050

At point C:

F(x, y) = 225(10) + 100(10) = $3250

At point D:

F(x, y) = 225(18) + 100(2) = $4250

The minimum cost is at point C(10, 10) which is $3250

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A rectangle has a length that is 3 more than the width. If the area of the rectangle is 28 units squared, what are the dimension
Alona [7]

you can think this

WL = 28

L=3w + 8

W( 3W +8) = 28

3 W^2 + 8W + = 28

3W^2 + 8W -28 = 0 (1)

3 W^2 - 6 W + !4 W -28 =0-

3 W ( W - 2 ) + 14 ( W -2) =0

(3W+ 14) ( w-2) = 0

w = 2 L = 3(2) + 8 = 14 , then LW =28

ignore the negative answer of w = -14/3

If we write all factors of 28 { 2, 4 , 7, 14)

We see that 28 = 2 * 14 , 14 = 2* 3 + 8

Therefore we can have a rectangle with area of 28 units, with 2, 14 be its dimension , and have the

property of L = 2*3 +8 (

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Nicole B. answered • 01/18/14

TUTOR 4.9 (82)

Change Challenges into SUCCESS! All Ages and Stages + TEST PREP

SEE TUTORS LIKE THIS

Hi Victoria,

Area=Length x width= 28 sq in

L=8+3w

So substitute that back into the equation:

Area = L x W

28 sq in = (8+3w) x w

28 sq in = 8w +3w2

28 sq in = w (8 + 3w)

Possible factors of 28 are 2 and 14 or 4 and 7, and 1 and 28. Substituting the possibilities in the equation, we find that the correct set of factors are 2 and (8 + 3*2) or 14.

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Arthur D. answered • 01/18/14

TUTOR 4.9 (67)

Mathematics Tutor With a Master's Degree In Mathematics

ABOUT THIS TUTOR ›

w=width

l=3w+8

A=l*w

28=(3w+8)(w)

28=3w^2+8w

3w^2+8w-28=0

(3w+14)(w-2)=0

3w+14=0

3w=-14

w=-14/3, disregard this answer because it is negative

w-2=0

w=2

l=3*2+8

l=14

check: 28=14*2=28

l=14 inches

w=2 inches

14 is 8 more than 3 times 2 !

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Tom D. answered • 01/18/14

TUTOR New to Wyzant

Very patient Math Expert who likes to teach

SEE TUTORS LIKE THIS

1) A=LW = 28 in

2) L = 3W + 8

Substitute L = 28/W into the 2nd equation

28/W = 3W + 8

28 = 3W^2 + 8W

3W^2 + 8W - 28 = 0

(3W+ 14)(W - 2) = 0

Note that the answer must be positive therefore the second 'zero' is the answer

4 0
3 years ago
Although still a sophomore at college, John O'Hagan's son Billy-Sean has already created several commercial video games and is c
Scilla [17]

Answer:

<em>27 feet for the south wall and 18 feet for the east/west walls</em>

Maximum area= 486\ ft^2

Step-by-step explanation:

<u>Optimization</u>

This is a simple case where an objective function must be minimized or maximized, given some restrictions coming in the form of equations.

The first derivative method will be used to find the values of the parameters that control the objective function and the maximum value of that function.

The office space for Billy-Sean will have the form of a rectangle of dimensions x and y, being x the number of feet for the south wall and y the number of feet for the west wall. The total cost of the space is

C=8x+12y

The budget to build the office space is $432, thus

8x+12y=432

Solving for y

\displaystyle y=\frac{432-8x}{12}

The area of the office space is

A=xy

Replacing the value found above

\displaystyle A=x\cdot \frac{432-8x}{12}

Operating

\displaystyle A= \frac{432x-8x^2}{12}

This is the objective function and must be maximized. Taking its first derivative and equating to 0:

\displaystyle A'= \frac{432-16x}{12}=0

Operating

432-16x=0

Solving

x=432/16=27

x=27\ feet

Calculating y

\displaystyle y=\frac{432-8\cdot 27}{12}

y=18\ feet

Compute the second derivative to ensure it's a maximum

\displaystyle A'= \frac{-16x}{12}

Since it's negative for x positive, the values found are a maximum for the area of the office space, which area is

A=xy=27\ ft\cdot 18\ ft\\\\\boxed{A=486\ ft^2}

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olga_2 [115]
As I already explained in previous answers for you, I'll just solve to make sure you're doing it correctly, y= -5/3 , as there is no b
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Lol accident oops no
wolverine [178]

Answer:

ahaha

Step-by-step explanation:

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The answer would be 173.42cm²
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