Top Brass Trophy Company, makes large championship trophies for youth athletic teams. At the moment they are planning production for fall sports: football and soccer. Each football trophy has a wood base, an engraved plaque, a large brass football on top, and returns $12 in profit. Soccer trophies are similar except that a brass soccer ball is on top, and the unit profit is only $9. Since the football has an asymmetric shape, its base requires 4 board feet of wood; the soccer base requires only 2 board feet. At the moment there are 1000 brass footballs in stock, 1500 soccer balls, 1750 plaques, and 4800 board feet of wood.

Required:
a. Define your decision variables and variable restrictions.
b. Build and present your linear programming model.
c. If you can, solve your linear programming model by graphical method. Otherwise, state your reason. Note that you can derive an optimal solution exactly by solving related equations.
d. If the number of available plaques is 200, modify your model and solve it again.

Answers

Answer 1

Answer:

a) maximize 12F + 9S

where:

F = football trophies

S = soccer trophies

b) constraints:

wood ⇒ 4F + 2S ≤ 4800

plaques ⇒ F + S ≤ 1750

brass footballs ⇒ F ≤ 1000

brass soccer balls ⇒ S ≤ 1500

c) using solver, the optimal solution is 650F + 1100S = $17,700

d) plaques ⇒ F + S ≤ 200, then

optimal solution is 200F = $2,400


Related Questions

Your god mother is baking a cake for your Halloween
party. She has a giant cake pan makes a cake four times
the size of any regular cake. The giant cake needs five
cups of flour. How many cups does a regular size cake
need?

Answers

Answer:

2

Step-by-step explanation:

Divide 4 into an even number, so its 2.

Answer:

1.25 or 1 and 1/4th

Step-by-step explanation:

you have to divide the cups of flower by the size of the pan

Enter the equivalent distance in km in the box.

1 km = 1000 m

1 m = 100 cm

35,000 cm =
km

Answers

Answer:

0.350 km

Step-by-step explanation:

Hi there !

35000 cm = 35000/100 m = 350 m

350 m = 350/1000 km = 0.350 km

Good luck !

in exercises 15-20 find the vector component of u along a and the vecomponent of u orthogonal to a u=(2,1,1,2) a=(4,-4,2,-2)

Answers

Answer:

The component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] is [tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex].

Step-by-step explanation:

Let [tex]\vec u[/tex] and [tex]\vec a[/tex], from Linear Algebra we get that component of [tex]\vec u[/tex] parallel to [tex]\vec a[/tex] by using this formula:

[tex]\vec u_{\parallel \,\vec a} = \frac{\vec u \bullet\vec a}{\|\vec a\|^{2}} \cdot \vec a[/tex] (Eq. 1)

Where [tex]\|\vec a\|[/tex] is the norm of [tex]\vec a[/tex], which is equal to [tex]\|\vec a\| = \sqrt{\vec a\bullet \vec a}[/tex]. (Eq. 2)

If we know that [tex]\vec u =(2,1,1,2)[/tex] and [tex]\vec a=(4,-4,2,-2)[/tex], then we get that vector component of [tex]\vec u[/tex] parallel to [tex]\vec a[/tex] is:

[tex]\vec u_{\parallel\,\vec a} = \left[\frac{(2)\cdot (4)+(1)\cdot (-4)+(1)\cdot (2)+(2)\cdot (-2)}{4^{2}+(-4)^{2}+2^{2}+(-2)^{2}} \right]\cdot (4,-4,2,-2)[/tex]

[tex]\vec u_{\parallel\,\vec a} =\frac{1}{20}\cdot (4,-4,2,-2)[/tex]

[tex]\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex]

Lastly, we find the vector component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] by applying this vector sum identity:

[tex]\vec u_{\perp\,\vec a} = \vec u - \vec u_{\parallel\,\vec a}[/tex] (Eq. 3)

If we get that [tex]\vec u =(2,1,1,2)[/tex] and [tex]\vec u_{\parallel\,\vec a} =\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex], the vector component of [tex]\vec u[/tex] is:

[tex]\vec u_{\perp\,\vec a} = (2,1,1,2)-\left(\frac{1}{5},-\frac{1}{5},\frac{1}{10},-\frac{1}{10} \right)[/tex]

[tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex]

The component of [tex]\vec u[/tex] orthogonal to [tex]\vec a[/tex] is [tex]\vec u_{\perp\,\vec a} = \left(\frac{9}{5},\frac{6}{5},\frac{9}{10},\frac{21}{10}\right)[/tex].

Suppose that you roll a die 8 times. What is the probability that you roll a six three or fewer times

Answers

Answer:

0.96

Step-by-step explanation:

Given that the a die is rolled 8 number of times.

[tex]n[/tex] = 8

Probability of getting a 6 on roll of a die,  [tex]p=\frac{1}{6}[/tex]

Probability of not getting a 6 on roll of a die,  [tex]q=1-p=1-\frac{1}{6}=\frac{5}{6}[/tex]

Probability of getting 6 three or fewer times:

[tex]P(r \le 3)=P(r=0)+P(r=1)+P(r=2)+P(r=3)[/tex]

Formula:

[tex]P(r=k)=_nC_k.p^k.q^{n-k}[/tex]

Putting the values using this formula:

[tex]P(r \le 3)=_8C_0.\frac{1}{6}^0.\frac{5}{6}^{8-0}+_8C_1.\frac{1}{6}^1.\frac{5}{6}^{8-1}+_8C_2.\frac{1}{6}^2.\frac{5}{6}^{8-2}+_8C_3.\frac{1}{6}^3.\frac{5}{6}^{8-3}\\\Rightarrow P(r \le 3)=1.\frac{5}{6}^{8}+8.\frac{1}{6}.\frac{5}{6}^{7}+28.\frac{1}{36}^2.\frac{5}{6}^{6}+56.\frac{1}{216}.\frac{5}{6}^{5}\\\Rightarrow P(r \le 3)=0.23+0.37+0.26+0.1=\bold{0.96}[/tex]

If f(x)=x^2 and g(x) =3x-1 find [g • f](x)

Answers

Answer:

3x²-1

Step-by-step explanation:

f(x) = x²

g(x) = 3x-1

[g·f](x)

g(f(x))

3(x²)-1

Explain how you would solve -5/8 divided by 2/3 and what the solution is?

Answers

Answer:

-15/16

Step-by-step explanation:

-5/8 ÷ 2/3

Copy dot flip

-5/8 * 3/2

Multiply the numerators

-5*3 = -15

Multiply the denominators

8*2 =16

Put the numerator over the denominator

-15/16

Hey now please just anser if itnus a try i will still give 5 stars. THE Question is what is the most easy way to SOLVE THE NINES TABLE IK THIS BUT I WANT to see who else knows sorry fir the big ketters i did not means to put that​

Answers

Answer:

Tbh, I think the easiest way is to count on your fingers. I still do it, however I can now do my chart tables to 17x17 by using fingers. People may tease, however, it is a good way to make sure you do not mess up as much as memorizing. You should memorize, and count on your fingers at the same time to solve extremely fast.

Step-by-step explanation:

9x4

You can pretend that your thumb equals nine, and count 9 plus 9 plus 9 plus 9, with each other finger, such as your ring finger, pointer, middle, and pinky , which equals 36. 5x9, you have five fingers on each hand, so each finger can equal nine (I don't care if people say that your thumb isn't a finger, just take it and move on lol).

Walt multiples 25 times 16 using partial products what did walt do wrong

Answers

Answer:

first what the full question and if 25*16/2=200

Step-by-step explanation:

The length of a rectangle is three times the width of the rectangle. The area of the rectangle is 48cm2. Draw the rectangle on the centimetre grid.

Answers

Answer:

The width is 4 cm

The length is 12 cm.

Step-by-step explanation:

Area of a rectangle

Given a rectangle of width W and length L, its area is calculated as follows:

[tex]A=W\cdot L[/tex]

The area of the given rectangle is 48 cm^2, and the length is three times the width, thus:

L = 3W

Substituting into the formula of the area:

[tex]W\cdot L=48[/tex]

[tex]W\cdot 3W=48[/tex]

Simplifying:

[tex]3W^2=48[/tex]

Solving:

[tex]W^2=48/3=16[/tex]

[tex]W=\sqrt{16}=4[/tex]

The width is 4 cm. Find the length:

L=3W=3*4= 12

The length is 12 cm.

The image attached shows the rectangle on the centimeter grid

Linearize the data. Then find the least squares regression equation

Answers

Answer:

C

Step-by-step explanation:

I will give brainliest :D

Which equation matches this scenario?

A family buys 8 tickets to a show. They also pay a $5
parking fee. They spend $61 to see the show.

• 5x+8=61
• 61+8x=5
• 8+5x=61
• 8x+5=61

Answers

8x+5=61 is the answer.

Answer: 8x + 5= 61

Step-by-step explanation: x represents the cost of one ticket for the show, 8 is the amount of tickets, 5 is the extra fee, 61 is the total.

Q13. A stone is dropped from a height of 5 km. The distance it falls through varies directly with the
square of the time taken to fall through that distance. If it falls 64 min 4 seconds. find the distance the
stone covers in the 5th second?
A. 36 m
B. 58 m
C. 72 m
D. 100 m

Answers

I’m not sure but I think it might be C so sorry if it’s wrong

Answer:

The stone covers 36 m in the 5th second. Correct choice: A.

Step-by-step explanation:

Proportions

Two variables are said to be proportional if one of them can be calculated by multiplying the other by a constant of proportionality. If y and x are those variables, then:

y=k.x

There are other similar proportions where the relation is not linear. For example, if y is proportional to the square of x, then:

[tex]y=k.x^2[/tex]

According to the conditions of the question, the distance traveled by a stone dropped from a height of 5 Km varies directly with the square of the time taken to fall through that distance. If d is the distance and t is the time, then;

[tex]d=k.t^2[/tex]

To find the value of k, we use the given condition: The stone falls d=66 meters in t=4 seconds. Substituting:

[tex]64=k.4^2=16k[/tex]

Solving:

[tex]k=64/16=4[/tex]

Substitute the value of k into the equation to get the complete model.

[tex]d=4.t^2[/tex]

Now we calculate the distance when t=5 seconds:

[tex]d=4\cdot 5^2=4\cdot 25=100[/tex]

The stone has covered 100 m in 5 seconds. But we need to find the distance covered in the 5th second, that specific interval between 4 sec and 5 sec.

Since we already know the distance for t=4 sec (64 m), and the distance for t=5 sec (100 m), then:

distance in the 5th second = 100 m - 64 m = 36 m

The stone covers 36 m in the 5th second. Option A.

FIRST RIGHT GETS BRAINLIEST

Answers

Answer:

-4+-6=-10

Step-by-step explanation:

6 TH grade math
On a hot day, Myra poured 4 1/8 buckets of water into a plastic wading pool. A few minutes later she added another 3 5/8 buckets. How much water did Myra pour into the pool?

Answers

Answer:

7 3/4

Step-by-step explanation:

4 1/8 + 3 5/8

Add the whole numbers, 4 + 3 = 7.

Add the fractions, 1/8 + 5/8 = 6/8.

You get 7 6/8. Simplify 6/8 to get 3/4.

Your answer is 7 3/4.

An airplane pilot over the Pacific sights a ship wreck at an angle of depression of 5°. At this time, the horizontal distance from the airplane to the wreck is 4629 meters. What is the height of the plane to the nearest meter?





405 m

Answers

Answer:

The height of the plane is 405 meters

Step-by-step explanation:

Trigonometric Ratios

The situation can be represented as shown in the image below. The ground, the height H, and the direct distance to the plane to the shipwreck form a right triangle, where the trigonometric ratios stand.

Since the known distance is adjacent to the angle, and the required height is opposite to the given angle, we use the tangent ratio, defined as:

[tex]\displaystyle \tan\ x=\frac{\text{opposite leg}}{\text{adjacent leg}}[/tex]

[tex]\displaystyle \tan 5^\circ=\frac{H}{4629}[/tex]

We need to find H, so we solve for H:

[tex]H=4629\cdot\tan5^\circ[/tex]

H=405 m

The height of the plane is 405 meters

please help meeeeeeeeeeeeee

Answers

D. alternate exterior angles. they are on the outsides and on opposite sides. hope this helps :)!!
It would be D hope this helps!

Mark reeds 42 pages of a book every 3/4 of an hour write an equation that models the relationship between Z, the number of hours mark reads, NY, the number of pages of the book He reads

Answers

Answer:

The equation that models the relationship between Z and N is N = 56 Z

Step-by-step explanation:

The form of the linear equation is y = m x + b, where

m is the rate ⇒ slopeb is the initial amount ⇒ y-intercept

∵ Mark reads 42 pages of a book every [tex]\frac{3}{4}[/tex] of an hour

→ Find his rate per hour by dividing the number of pages by its time

His rate of reading = 42 ÷  [tex]\frac{3}{4}[/tex] = 42 ×  [tex]\frac{4}{3}[/tex] = 56 pages per hour

∵ His rate = 56 pages/hour

m = 56

Z represents the number of hours Mark reads

→ That means replace x in the form of the equation above with Z

N represents the number of pages of the book he reads

→ That means replace y in the form of the equation above with N

∴ N = 56 Z + b

There is no initial amount of reading

b = 0

N = 56 Z

The equation that models the relationship between Z and N is N = 56 Z

What is the slope of the points (2,5) and (0,-4)?

Answers

To find the slope of two points, we have to first assign our points as x1, y1 and x2, y2.

In our problem,

x1 = 2 and y1 = 5

x2 = 0 and y2 = -4

We know that that slope = y2 - y1 / x2 - x1. Let's plug our numbers into this formula.

Slope = -4 - 5 / 0 - 2 = -9 / -2 = 9 / 2

A florist must make 5 identical
bridesmaid bouquets for a wedding. The budget is
$160, and each bouquet must have 12 flowers. Roses
cost $2.50 each, lilies cost $4 each, and irises cost
$2 each. The florist wants twice as many roses as the
other two types of flowers combined.

Answers

Answer:

A. 40x + 10y + 10z = $160

B. 8 Roses, 2 lilies and 2 irises

C.

1. 20x + 5y + 5z = $80

2. 4x + y + z = $16

3. 8x + 2y + 2z = $32

Step-by-step explanation:

Cost for each flower = $160/5 = $32

So we have $32 for each bouquet consisting of 12 flowers each.

Roses = x = $2.50 each

lilies = y = $4 each

irises = z = $2 each

8x + 2y + 2z = $32

8($2.50) + 2($4) + 2($2) = $32

$20 + $8 + $4 = $32

$32 = $32

a. Maximum budget is $160

40x + 10y + 10z = $160

40($2.50) + 10($4) + 10($2) = $160

$100 + $40 + $20 = $160

$160 = $160

b. From above

8x + 2y + 2z = $32

8 Roses, 2 lilies and 2 irises

c. No. There are other solutions If total cost is not limited

1. 20x + 5y + 5z

20($2.50) + 5($4) + 5($2)

$50 + $20 + $10

= $80

2. 4x + y + z

4($2.50) + $4 + $2

$10 + $4 + $2

= $16

3. 8x + 2y + 2z

8($2.50) + 2($4) + 2($2)

$20 + $8 + $4

= $32

show that: (1-sin x)/(cos x)=(sec x - tan x)​

Answers

This is the step-by-step explanation

Review the proof of de Moivre’s theorem (not in order).

Proof of de Moivre's Theorem
[cos(θ) + isin(θ)]k + 1
A = [cos(θ) + isin(θ)]k ∙ [cos(θ) + isin(θ)]1
B = cos(kθ + θ) + isin(kθ + θ)
C = cos(kθ)cos(θ) − sin(kθ)sin(θ) + i[sin(kθ)cos(θ) + cos(kθ)sin(θ)]
D = [cos(kθ) + isin(kθ)] ∙ [cos(θ) + isin(θ)]
E = cos[(k + 1)θ] + isin[(k + 1)θ]
Which steps must be switched to put the proof in order?

steps B and C
steps B and D
steps C and D
steps C and E

Answers

Answer:

steps B and D

Step-by-step explanation:

the correct chart is below :)

The steps which must be switched to put the proof in order are steps B and D

Since [cos(θ) + isin(θ)]k + 1

= [cos(θ) + isin(θ)]k ∙ [cos(θ) + isin(θ)]1

= [cos(kθ) + isin(kθ)] ∙ [cos(θ) + isin(θ)]

= cos(kθ)cos(θ) − sin(kθ)sin(θ) + i[sin(kθ)cos(θ) + cos(kθ)sin(θ)]

= cos(kθ + θ) + isin(kθ + θ)

= cos[(k + 1)θ] + isin[(k + 1)θ]

Since the step after A is [cos(kθ) + isin(kθ)] ∙ [cos(θ) + isin(θ)] = D, and the step after C is cos(kθ + θ) + isin(kθ + θ) = B.

So, steps B and D must be switched.

The steps which must be switched to put the proof in order are steps B and D.

Learn more about De Moivre's theorem here:

https://brainly.com/question/11889817

Which is a correct way to subtract from a number? (A). Add 100 then subtract 1 (B). Add 100 then add 2. (C). Subtract 100 then add 2 (D). Subtract 100 then add 1.

Answers

Answer:

A is the answer

Step-by-step explanation:

According to BODMAS (or DMAS), first we add and then subtract

if both operations are of add, we add it at the same time

34(8x – 6) – 2 = 12 – x

Answers

Answer:

sorry for my handwriting

i think this is the correct answer

The R.D. Wilson Company makes a soft drink dispensing machine that allows customers to get soft drinks from the machine in a cup with ice. When the machine is running properly, the average number of fluid ounces in the cup should be 14. Periodically the machines need to be tested to make sure that they have not gone out of adjustment. To do this, six cups are filled by the machine and a technician carefully measures the volume in each cup. In one such test, the following data were observed:_______.
14.25 13.7 14.02
14.13 13.99 14.0
Based on these sample data,which of the following is true if the significance level is .05?
A) No conclusion can be reached about the status of the machine based on a sample size of only six cups.
B) The null hypothesis cannot be rejected since the test statistic is approximately t = .29,which is not in the rejection region.
C) The null hypothesis can be rejected since the sample mean is greater than 14.
D) The null can be rejected because the majority of the sample values exceed 14.

Answers

Answer:

The null hypothesis cannot be rejected since the test statistic is approximately t = .20,which is not in the rejection region.

Step-by-step explanation:

Data: 14.25, 13.7, 14.02,  14.13, 13.99, 14.0

Mean = [tex]\frac{Sum}{n}=14.015[/tex]

Standard deviation =[tex]\sqrt{\frac{\sum(x-\bar{x})^2}{n}}=0.1836[/tex]

Claim : Average number of fluid ounces in the cup should be 14.

Null hypothesis : [tex]H_0:\mu = 14[/tex]

Alternate hypothesis :[tex]H_a:\mu \neq 14[/tex]

n = 6

[tex]t = \frac{x-\mu}{\frac{s}{\sqrt{n}}}\\t=\frac{14.015-14}{\frac{0.1836}{\sqrt{6}}}\\t=0.20\\\alpha = 0.05t_{df,\alpha}=t_{(5,0.05)}=2.571[/tex]

t critical > t calculated

So, we failed to reject null hypothesis

So, Option B is true

Hence The null hypothesis cannot be rejected since the test statistic is approximately t = .20,which is not in the rejection region.

what is the rate of change for the liner relationship modeled in the table?

Answers

i'm sorry wheres the picture?

Show me the picture I would love to help <3

I WILL BRAINLIST ITS ONLY ONE PROBLEM !!!!!!!!!!!!!!!

Answers

Answer:

11/200

Step-by-step explanation:

This is the correct answer boo

11/200 is the answer lol

There are (26)3⋅ 20 bacteria in a sample. What is the total number of bacteria in the sample? (1 point)

Answers

Answer: If we multiply then I guess it’s 26*3=78 and 78*20=1,560

Step-by-step explanation:

5x-(x+3)=1/3(9x+18)-5

Answers

Answer: x=4

Step-by-step explanation:

The answer is 4 once simplified in

Mary used 1/2 of a can of paint to cover 1/8 of the outside of her house. How many cans of paint will Mary need to cover the entire outside of her house?

Answers

Answer:

4 cans of paint

Step-by-step explanation:

Half of a can = 1/8 of the outside of the house.

2 halves = whole can of paint

8/2=4

4 cans of paint

fplzz ans my question
factorize p^4+4​

Answers

Answer:

Step-by-step explanation:

(p²)²+2²

(p²+2)²-2p²2

(p²+2)²-4p²

(p²+2)²-(2p)²

(p²+2-2p)(p²+2+2p)

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