The Pitts Barbecue Company makes three kinds of barbecue sauce: Extra Hot, Hot, and Mild. Pitts’ vice president of marketing estimates that the company can sell 8,000 cases of its Extra Hot sauce plus 10 extra cases for every dollar it spends promoting this sauce; 10,000 cases of Hot sauce plus 8 extra cases for every dollar spent promoting this sauce; and 12,000 cases of its Mild sauce plus 5 extra cases for every dollar spent promoting this sauce. Although each barbecue sauce sells for $10 per case, the cost of producing the different types of sauce varies. It costs the company $6 to produce a case of Extra Hot sauce, $5.50 to produce a case of Hot sauce, and $5.25 to produce a case of Mild sauce. The president of the company wants to make sure the company manufactures at least the minimum amounts of each sauce that the marketing vice president thinks the company can sell. A budget of $25,000 total has been approved for promoting these items of which at least $5,000 must be spent advertising each item. How many cases of each type of sauce should be made, and how do you suggest that the company allocate the promotional budget to maximize profits?

a. Formulate an LP model for this problem.
b. Create a spreadsheet model for this problem, and solve it using Solver.
c. What is the optimal solution?

Answers

Answer 1

Answer:

Case of Extra hot sauce     8000 cases

Case of Hot Sauce            10000 cases

Case of Mild Sauce           12000  + 2000 =  14000

z´(max) =  143500 $

Step-by-step explanation:

Profit of each product:

                                                     sale price $     cost  $       Profit $

Case of Extra hot sauce                       10                6                  4

Case of Hot Sauce                                10                5.5               4.5

Case of Mild Sauce                               10                5.25             4.75

The President of the company already orders the minimum of each case of sauce  as follows:

Case of Extra hot sauce  8000

Case of Hot Sauce          10000

Case of Mild Sauce        12000

Let´s call

x₁ quantity of cases of Case of Extra hot sauce  over 8000 cases

x₂ quantity of cases of Case of hot sauce  over 10000 cases

x₃ quantity of cases of Case of mild sauce  over 12000 cases

Then Objective function will be:

z  =  4*x₁  +  4.5*x₂  + 4.75*x₃    to maximize

Promoting budget constraint:

each dollar investing in promoting x₁   will become  10*x₁  ( cases)

each dollar investing in promoting x₂   will become   8*x₂(cases )

each  dollar investing in promoting x₃   will become  5*x₃ ( cases)

Total investment in promotion is 10000 $ again here we need by sure to invest 5000 $ in promotion for each type of sauce, leaving only extra 10000 $, then:

Constraint due to promotional budge:

10*x₁  +  8*x₂  +  5*x₃  ≤  10000

General constraints:

x₁  ≥  0     x₂  ≥0     x₃   ≥  0   all integers

Then the model  is:

z  =  4*x₁  +  4.5*x₂  + 4.75*x₃    to maximize

Subject to:

10*x₁  +  8*x₂  +  5*x₃  ≤  10000

x₁  ≥  0     x₂  ≥0     x₃   ≥  0   all integers

After 6 iterations using an on-line solver we got optimal solution:

x₁  =  x₂  =  0     x₃ = 2000

z(max) =  9500 $

Then as previous comments, the production will be:

Case of Extra hot sauce     8000 +  0   =  8000

Case of Hot Sauce            10000  +  0  =  10000

Case of Mild Sauce           12000  + 2000 =  14000

The whole profits :

z´  =  4*8000  + 4.5*10000 +  4.75 ( 12000 + 2000)

z´(max) = 32000 + 45000 +  66500

z´(max) = 143500 $

Aditional comments:

If we have n products at the same price it looks obvious that we manufacture the one wich the lowest cost. In this problem, the sales price is the same for the three sauces, and the production cost is the lowest for the Mild sauce, therefore as a consequence, it will be more profitable to manufacture Mild sauce.


Related Questions

Find the distance between A(-3, 2) and B(5, -1).

Answers

the distance between those two points would be (8,-3)

1. A drama club earned $662.50 from a production where 85 adult tickets were sold and 65
student tickets were sold. An adult ticket costs $2.50 more than a student ticket. Which
system of equations can be used to find a, the cost of an adult ticket, and s, the cost of a
student ticket?

Answers

Answer: The cost of adult ticket is $6.1 and that of student ticket is $2.44

Step-by-step explanation:

Let the cost of adult ticket be 'x' and cost of student ticket be 'y'

From the question, the equations formed are:

[tex]662.5=85x+65y[/tex]                .....(1)

[tex]x=2.5y[/tex]                                ......(2)

Putting value of 'y' from equation 2 to equation 1:

[tex]662.5=85(2.5x)+65y\\\\662.5=271.5y\\\\y=\frac{662.5}{271.5}=\$ 2.44[/tex]

Now, solving for 'x', we get:

[tex]x=2.5(2.44)=\$ 6.1[/tex]

Hence, the cost of adult ticket is $6.1 and that of student ticket is $2.44

you and your friend start biking to opposite directions from the same point. You travel 108 feet every 8 seconds. Your friend travels 63 feet every 6 seconds. a) how far apart are you and your friend after 15 minutes? b) after 20 minutes you take a 5- minutes rest, but your friend does not. How far apart are you and your friend after 40 minutes? Explain your reasoning.

Answers

Answer:

To find your distance apart, you can convert 15 minutes to seconds because that is what the rate is given in.

15 mins x 60 seconds = 900 seconds.

Step-by-step explanation:

In 900 seconds, there are 900/8=112.5 groups of 8 seconds. This means there are 112.5 groups of 108 feet.

112.5 x 108 = 12150 feet

12150 feet/5280 feet is approximately 2.3 miles.

For your friend you take 900/6 = 150 groups of 6 seconds.

150 x 63 = 9540 feet

9540 feet/5280 feet = 1.79 miles

1.79 miles + 2.3 miles = 2.09 miles

You and your friend are about 2.09 miles apart after 15 minutes.

B). If you go 2.3 miles every 15 minutes, that means you travel about 0.77 miles every 5 minutes. If you travel 20 more minutes (40-15-5) that would be 0.77x 4=3.07 miles more

3.07 + 2.3 = 5.37 miles after 40 minutes (you).

Your friend travels 1.79 in 15 minutes, so 1.79/3 = 0.6 miles every 5 minutes

0.6 x 5 (5 x 5 = 25 minutes)= 3 miles

1.79 + 3 miles= 4.79 miles (friend)

4.79 + 5.37 = 10.16 miles

You and your friend are about 10.16 miles apart after 40 minutes.

Raw scores on behavioral tests are often transformed for easier comparison. A test of reading ability has mean 67 and standard deviation 10 when given to third graders. Sixth graders have mean score 86 and standard deviation 9 on the same test. To provide separate "norms" for each grade, we want scores in each grade to have mean 100 and standard deviation 20. (Round your answers to two decimal places.)
(a) What linear transformation will change third-grade scores x into new scores xnew = a + bx that have the desired mean and standard deviation? (Use b > 0 to preserve the order of the scores.) a = b = (b)
Do the same for the sixth-grade scores.
a =
b =
(c) David is a third-grade student who scores 79 on the test. Find David's transformed score.
Nancy is a sixth-grade student who scores 79. What is her transformed score?
Who scores higher within his or her grade? Nancy or David

Answers

Answer:

a.) a = -34 and b = 2

b.) a = -91.11 b = 2.22

c.) David scored 124, nancy scored 84.27

David scored higher

Step-by-step explanation:

for those in the 3rd grade

mean u = 67

s = 10

we used the z formula

[tex]z=\frac{x-u}{s}[/tex]

[tex]z=\frac{x-67}{10}[/tex]

we have the new score

u = 100

s = 20

we use this formula [tex]z*s+u[/tex]

[tex][\frac{x-67}{10} ]20\\[/tex] + 100

multiply through by 20

[tex][\frac{20x-1340}{10} ] +100[/tex]

dividing the bracket by 10

= [tex]2x-134+100[/tex]

= [tex]2x-34[/tex]

from this solution above,

a = -34 and b = 2

b.)

we solve for those in the 6th grade

u = 86

s = 9

[tex]\frac{x-86}{9}[/tex]

for new score,

y = 100

s = 20

[tex][\frac{x-86}{9} ]20+100[/tex]

[tex]2.22x-191.11+100\\= 2.22x - 91.11[/tex]

from this solution

a = -91.11

b = 2.22

c.) if David scored 79

[tex]= 2(x)-34[/tex]

= 2(79) - 34

= 158 - 34

= 124

if nancy scored 79

= 2.22(79) - 91.11

= 175.38 - 91.11

= 84.27

from these scores we can see that David scored higher in his grade

identify the angle type, then find the value of x

Answers

9514 1404 393

Answer:

acute anglex = 25

Step-by-step explanation:

The angle shown is 75°. It is less than 90°, so is an acute angle. (The diagram is misleading in that respect.)

__

The two marked angles are vertical angles, so have the same measure.

  3x° = 75°

  x = 25 . . . . . . . . divide both sides by 3°

Are the triangles congruent? Why or why not?

Answers

Answer:

ffffffssssssssssssssssscv

Step-by-step explanation:

yes i believe so because angle A and D are congruent, therefore the same, and the yellow side is in the same place :))

Solve the following system of equations with the substitution method.
{x+y=25
y=4x
(x,y)=( , )

Answers

Answer:

(5,20)

Step-by-step explanation:

x+y=25

If you substitute y=4x,

x+4x=25

Now add like terms

5x=25

Divide 5

x=5

Put it back into the equation

5+y=25

Subtract 5

y=20

Answer: (5,20)

please help quick!!!

Answers

I couldn’t help because I can’t see the equations below

You are told that a random sample of 150 people from Manchester New Hampshire have been given cholesterol tests, and 60 of these people had levels over the "safe" count of 200. Construct a 95% confidence interval for the population proportion of people in New Hampshire with cholesterol levels over 200.

Answers

Answer:

The 95% confidence interval for the population proportion of people in New Hampshire with cholesterol levels over 200 is (0.3216, 0.4784).

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 z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].

You are told that a random sample of 150 people from Manchester New Hampshire have been given cholesterol tests, and 60 of these people had levels over the "safe" count of 200.

This means that [tex]n = 150, \pi = \frac{60}{150} = 0.4[/tex]

95% confidence level

So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].

The lower limit of this interval is:

[tex]\pi - z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 - 1.96\sqrt{\frac{0.4*0.6}{150}} = 0.3216[/tex]

The upper limit of this interval is:

[tex]\pi + z\sqrt{\frac{\pi(1-\pi)}{n}} = 0.4 + 1.96\sqrt{\frac{0.4*0.6}{150}} = 0.4784[/tex]

The 95% confidence interval for the population proportion of people in New Hampshire with cholesterol levels over 200 is (0.3216, 0.4784).

Help me asap!!pleaseeee

Answers

Answer:

a

Step-by-step explanation:

yes

Which is the graph of an even monomial function?

Answers

Answer:

The graph of an even function is symmetric about the y-axis. The graph of an odd function is symmetric about the x-axis. It is possible that the use of these two words originated with the observation that the graph of a polynomial function in which all variables are to an even power is symmetric about the y -axis.

Given: x - 6 ≤ 1. Choose the solution set.

Answers

Answer:

x<7

Step-by-step explanation:

See image below:)

libreng puntoss
yeeah​

Answers

THANK YOU PO

PA BRAINLIEST

Your dog is so cute I wish I had one

The circle above has a radius of 7 cm. What is the area of the circle

Answers

Answer:

153.86 cm²

Step-by-step explanation:

Area circle = πr²

Area = 3.14 * 7²

Area = 3.14 * 49

Area = 153.86

If my answer is incorrect, pls correct me!

If you like my answer and explanation, mark me as brainliest!

-Chetan K

A research team conducted a study showing that approximately 30% of all businessmen who wear ties wear them so tightly that they actually reduce blood flow to the brain, diminishing cerebral functions. At a board meeting of 30 businessmen, all of whom wear ties, what are the following probabilities?

a. at least one tie is too tight
b. more than two ties are too tight
c. no tie is too tight
d. at least 18 ties are not too tight

Answers

Answer:

a) 0.9998

b) 0.9979

c) 0.7

d) 0.9155

Step-by-step explanation:

P( people who wear their ties tightly ) = 0.3

P( people who do not wear their ties tightly ) = 1 - 0.3 = 0.7

sample size ( n ) = 30

Given that the events are independent and there are only two outcomes we will apply Binomial distribution

a) P( at least one tie is too tight )

P ( x ≥ 1 ) = 1 - P ( x < 1 ) = 1 - P ( x = 0 )

       = 1 - 0.00002 = 0.9998 ( excel function: 1 - BINOMDIST(0,30,0.3,0) )

b) P( more than two ties are too tight )

P ( x > 2 ) = 1 - P ( x ≤ 2 ) = 1 - BINOMDIST(2, 30, 0.3, 1 )

                                       = 1 - 0.002113178

                                       = 0.9979

c) P ( no tie is tight )

P ( x = 0 ) = 0.7

d) P( at least 18 ties are not too tight )    i.e. ( P = 0.7 )

   P ( x ≥ 18 ) = 1 - P( x ≤  17 )

                     = 1 - BINOMDIST ( 17, 30, 0.7, 1 )

                     = 1 -  0.08447006

                    = 0.9155

Which of the following are mutually exclusive events?
A. An athlete being 5 feet tall and 6 feet tall
B. A student belonging to the chess club and the math club
C. A person having brown eyes and brown hair
D. A teacher teaching English composition and English literature

Answers

Answer: A

Step-by-step explanation: Ape x

help me please geometry!!

Find the missing side length.

Answers

Set up a ratio:

16/12 = 28/?

Cross multiply:

16? = 12 x 28

16? = 336

Divide both sides by 16:

? = 336/16

? = 21

will mark brainliest

Answers

Answer:

(x, y) = (-2,-5)

Step-by-step explanation:

Multiply the first equation by 3,and multiply the second equation by 1.

3(3x+y=−11)

1(4x−3y=7)

Becomes:

9x+3y=−33

4x−3y=7

Add these equations to eliminate y:

13x=−26

Then solve13x=−26for x:

13x=−26

13x

13

=

−26

13

(Divide both sides by 13)

x=−2

Now that we've found x let's plug it back in to solve for y.

Write down an original equation:

3x+y=−11

Substitute−2forxin3x+y=−11:

(3)(−2)+y=−11

y−6=−11(Simplify both sides of the equation)

y−6+6=−11+6(Add 6 to both sides)

y=−5

Answer:

x=−2 and y=−5

As shown in the diagram below, AABC - A DEF, AB=14, BC=4, DE=7, and EF = X
D
14
B
4
С
E
X
F
What is the length of EF?
А
28
B
14
2
4

Answers

Answer:

EF=4

Step-by-step explanation:

vì diện tích bằng nhau và bằng 28 áp dụng công thức tính diện tích

I’ll mark brainliest

Answers

Answer:

[tex]\text{A. }y=1.30x+1.50[/tex]

Step-by-step explanation:

The two ringtones will cost her a total of [tex]0.75\cdot 2=1.50[/tex] and is a fixed amount. The relationship between the cost and number of songs only is [tex]y=1.30x[/tex] and therefore the answer is [tex]\boxed{\text{A. }y=1.30x+1.50}[/tex]. You can also directly find the answer by finding the y-intercept (in this case [tex]1.50[/tex]), as no other answer choices include the term [tex]1.50[/tex], so A must be the correct answer.

I’ll mark you as brainliest

Answers

Step-by-step explanation:

1) -5n+10n

= 5n

2) -x-9+2x-10

= 2x-x-9-10

= x-19

3) -5(x-10)-x

= -5x+50-x

= -6x+50

4) 9-5(1-7x)

= 9-5+35x

= 35x+4

5) y^2-x

= 3^2-2

= 9-2

= 7

Do the remain questions by yourself, you can do it!

A rectangle is 9 inches long and 3x inches wide. The value of the perimeter (in inches) is equal to the value of the area (in square inches).
Find x

Answers

Answer:

3

Step-by-step explanation:

The perimeter of the rectangle is equal to the doubled sum of the sides, and the area is equal to the product of the sides. So we have the following equation

X is 3, hope that helps!

Suppose that the logons to a computer network follow a Poisson process with an average of 3 logons per minute. (a) What is the mean time between logons (in minutes)

Answers

Answer:

The mean time between logons is of 0.3333 minutes.

Step-by-step explanation:

Poisson process with an average of 3 logons per minute.

This means that the time between logons follows an exponential distribution, which mean is given by:

[tex]E(X) = \frac{1}{\lambda}[/tex]

For this question, we have that [tex]\lambda = 3[/tex], and thus:

[tex]E(X) = \frac{1}{\lambda} = \frac{1}{3} = 0.3333[/tex]

The mean time between logons is of 0.3333 minutes.

What is the density of this object? (A sphere)​

Answers

9514 1404 393

Answer:

  about 0.299 kg/m³

Step-by-step explanation:

Density is the ratio of mass to volume.

  ρ = M/V

  ρ = (10 kg)/(4/3π(2 m)³) = 15/(16π) kg/m³ ≈ 0.299 kg/m³

Find the surface area of the
prism.

Answers

Answer:

Area of front and back = 2 * 2 * 5 = 20 cm^2

Area of sides = 2 * 3 * 4 = 24 cm^2

Area of top and bottom = 2 * 4 * 5 = 40 cm^2

TOTAL area = 84 cm^2

Step-by-step explanation:

Total area = 84cm squared

which term in the quotient of this expression contains an error?

Answers

Answer:

The + 78 :-  it should be + 60.

Step-by-step explanation:

Long division:-

x - 3 )4x^4 - 6x^3 + 0x^2 + 6x + 3 ( 4x^3 + 6x^2 + 18x + 60 <--- Quotient.

         4x^4 - 12x^3

                      6x^3 + 0x^2

                       6x^2 - 18x^2

                                   18x^2 + 6x

                                    18x^2 - 54x

                                                 60x + 3

                                                  60x - 180

                                                              183

Dan's car depreciates at a rate of 7% per year.
By what percentage has Dan's car depreciated after 6 years?
Give your answer to the nearest percent.

Answers

Answer:

20%

Step-by-step explanation:

Given that

The car is depreciated at a rate of 7% per year

We need to find out the percentage when the car is depreciated after 6 years

So,

Since the car is depreciated by 7% so we can say it can be 0.93 times in a year

Now after 6 years, it would make

= 0.93^3

= 0.80

So, the percentage is

= 1 - 0.80

= 0.20

= 20%

For any exponential function of the form f(x) = a · b^x where b≠0, what is the y-intercept of the graph of f(x)?

(0,a)
(1,0)
(a,0)
(0,1)

Answers

Answer:

1) (0,a)

Step-by-step explanation:

f(0) = a. b^0 = a. 1 = a

=> (0,a)

The ratio of winners to losers was 7 to 5. If the total number of winners and losers was 1260, how many more winners were there than losers?​

Answers

Answer:

210

Step-by-step explanation:

7:5

First add the ratios

7+5=12

Put each ratio over the denominator 12 then multiply each by the total

7/12×1260= 735

5/12 × 1260 = 525

To find how many more winners than losers

735-525= 210

Which drink has more sugar per fluid ounce? 50 POINTS

Answers

it would be drink a.
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