1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
ycow [4]
2 years ago
13

The Beef-up ranch feeds cattle for midwestern farmers and delivers them to processing plants in Topeka,Kansas and Tulsa, Oklahom

a. The ranch must determine the amounts of catlle feed to buy so that variouis nutritional requirements are met while minimizing total feed costs. The mixture fed to the cows must contain different levels of four key nutrients and can be made by blending three different feeds. The amount of each nutrient (in ounces) found in each pound of feed is summarized as follows:
Nutrient a- feed 1 (3) feed 2 (2) feed 3 (4)

b- feed 1 (3) feed 2 (1) feed 3 (3)

c- feed 1 ( 1) feed 2 (0) feed 3 (2)

d- feed 1 (6) feed 2 (8) feed 3 (4)

The cost per pound of feeds 1,2, and 3 are $2.00, $2.50, and $3.00, respectively. The minimum requirement per cow each month is 4 pounds of nutrient A, 5 pounds of nutrient B, 1 pound of nutrient C, and 8 pounds of nutrient D. However, cows should not be fed more than twice the minimum requirement for any nutrient each month. Additionally, the ranch can only obtain 1,500 pounds of each type of feed each month. Because there aree usually 100 cows at the beef-up ranch at any given time, this means that no more than 15 pounds of each type of feed can be used per cow each month.

a. Formulate a linear programming problem to determine how much of each type of feed a cow should be fed each month.

b. Create a spreadsheet model for this problem, and solve it using Solver

c. what is the optimal solution?
Business
1 answer:
AfilCa [17]2 years ago
4 0

Answer:

a. Min Z = 2x₁ + 2.50x₂ + 3x₃

Subject to constraints :

3x₁ + 2x₂ + 4x₃ ≤ 128           .......(1)

3x₁ + x₂ + 3x₃ ≤ 160             ........(2)

x₁ + 0x₂ + 2x₃ ≤ 32              .........(3)

6x₁ + 8x₂ + 4x₃ ≤ 256          .........(4)

3x₁ + 2x₂ + 4x₃ ≥ 64            ..........(5)

3x₁ + x₂ + 3x₃ ≥ 80              ..........(6)

x₁ + 0x₂ + 2x₃ ≥ 16              ...........(7)

6x₁ + 8x₂ + 4x₃ ≥ 128         ............(8)

x₁ ≤ 15                                 ...........(9)

x₂≤ 15                                  ...........(10)

x₃ ≤ 15                                 ...........(11)

x₁ , x₂, x₃ ≥ 0

b. x₁ = 15 ,  x₂ = 9.5 , x₃ = 8.5

c. The optimal solution is Z = 79.25

Explanation:

Given - The table is as follows :

  • Nutrient           Feed 1                    Feed 2                      Feed 3
  •    A                      3                              2                                4
  •    B                      3                               1                                 3
  •    C                      1                                0                                2
  •    D                      6                               8                                4

The minimum requirement per cow each month is 4 pounds of nutrient A, 5 pounds of nutrient B, 1 pound of nutrient C, and 8 pounds of nutrient D. However, cows should not be fed more than twice the minimum requirement for any nutrient each month. Additionally, the ranch can only obtain 1,500 pounds of each type of feed each month. Because there are usually 100 cows at the beef-up ranch at any given time, this means that no more than 15 pounds of each type of feed can be used per cow each month.

To find - a. Formulate a linear programming problem to determine how  

                  much of each type of feed a cow should be fed each month.

              b. Create a spreadsheet model for this problem, and solve it using

                   Solver.

              c. What is the optimal solution?

Proof -

a.

Let feed 1 per cow per month = x₁

     feed 2 per cow per month = x₂

     feed 3 per cow per month = x₃

Now,

As given, The cost per pound of feeds 1,2, and 3 are $2.00, $2.50, and $3.00, respectively.

So, we have to minimize the cost , Z = 2x₁ + 2.50x₂ + 3x₃

Subject to constraints :

3x₁ + 2x₂ + 4x₃ ≤ 4(32)

3x₁ + x₂ + 3x₃ ≤ 5(32)

x₁ + 0x₂ + 2x₃ ≤ 1(32)

6x₁ + 8x₂ + 4x₃ ≤ 8(32)

∴ we get

Min Z = 2x₁ + 2.50x₂ + 3x₃

Subject to constraints :

3x₁ + 2x₂ + 4x₃ ≤ 128           .......(1)

3x₁ + x₂ + 3x₃ ≤ 160             ........(2)

x₁ + 0x₂ + 2x₃ ≤ 32              .........(3)

6x₁ + 8x₂ + 4x₃ ≤ 256          .........(4)

Now, as given

However, cows should not be fed more than twice the minimum requirement for any nutrient each month.

∴ we have

3x₁ + 2x₂ + 4x₃ ≥ \frac{128}{2}

3x₁ + x₂ + 3x₃ ≥ \frac{160}{2}

x₁ + 0x₂ + 2x₃ ≥ \frac{32}{2}

6x₁ + 8x₂ + 4x₃ ≥ \frac{256}{2}

and also

No more than 15 pounds of each type of feed can be used per cow each month.

⇒x₁ , x₂, x₃ ≤ 15

So,

The LPP model becomes

Min Z = 2x₁ + 2.50x₂ + 3x₃

Subject to constraints :

3x₁ + 2x₂ + 4x₃ ≤ 128           .......(1)

3x₁ + x₂ + 3x₃ ≤ 160             ........(2)

x₁ + 0x₂ + 2x₃ ≤ 32              .........(3)

6x₁ + 8x₂ + 4x₃ ≤ 256          .........(4)

3x₁ + 2x₂ + 4x₃ ≥ 64            ..........(5)

3x₁ + x₂ + 3x₃ ≥ 80              ..........(6)

x₁ + 0x₂ + 2x₃ ≥ 16              ...........(7)

6x₁ + 8x₂ + 4x₃ ≥ 128         ............(8)

x₁ ≤ 15                                 ...........(9)

x₂≤ 15                                  ...........(10)

x₃ ≤ 15                                 ...........(11)

x₁ , x₂, x₃ ≥ 0

b.)

We use simplex method calculator  to solve this LPP Problem

we get

x₁ = 15 ,  x₂ = 9.5 , x₃ = 8.5

c.)

The optimal solution is Z = 79.25

You might be interested in
Hal Gore won a $2.1 million prize for special contributions to environmental research. This prize is awarded for public achievem
ioda

Answer:

1.53 Million

Explanation:

The reason is that the Environment Protection Agency is a qualified organization and donations made to qualified organization are allowable expense under the US tax rules, so the gross income will include a net amount which is the actual amount left for Hal Gore and which is $1.53 million ($2.1 m - 0.57).

8 0
3 years ago
Assume you own and operate a small advertising business that employs 25 people. With increased health care costs and related ins
Tcecarenko [31]

Answer: (C) Safety and security needs

Explanation:

  The Safety and the security needs are one of the type of Maslow's hierarchy model that helps us to protect from the job security, safe and the healthy environment. The safety and the security are the basic physiological needs that is necessary for survival to each person.

 According to the given question, the decision made by an organization may cause the employees concerned about their safety and the various types of security requirement as employees can concentrate on given task in the healthy work environment only.

 It is also helps in increase the productivity as well as growth of the business and an organization. Therefore, Option (C) is correct answer.      

 

5 0
3 years ago
Mrs. Patterson is a new enrollee in the HealthBest Medicare Advantage (MA-PD) plan. She is new to this type of coverage and asks
Serggg [28]

Answer:

She should expect either the pharmacy directory in hard copy or a distinct and separate notice (in hard copy) describing where she can find the pharmacy directory online and how to request a hard copy.

Explanation:

Additionally, I will also mention that The main difference between medicare advantage plan and Normal medicare is that normal medicare will include wide coverage provided by the government, but the quality of services provided for the medicare advantage plan will be better on average.

The pharmacy directory mentioned above can be used by Mrs. Patterson to choose the type of Specific health services that she wants, the type of specialists that she prefers and the location of treatment that is the most convenient to her. (this type of benefits wouldn't be found in normal plan)

5 0
2 years ago
For marketing to occur, there must be two or more parties with unsatisfied needs. Dr. Pepper Snapple Group distributes Country T
Len [333]

Answer:

The answer to this question is

b. people with a desire for a beverage other than soda or water

Explanation:

The "second" party needed for marketing to occur in this case are people who are in need of the product produced by Dr. Pepper Snapple Group. (I.e the customers ) however, the type of customer that Dr. Pepper Snapple group will seek to have are customer with a desire for a beverage other than soda and water because it's price is comparable to that of soft drink.  Which implies that customer with no interest in that kind of  product will not buy but will rather stick with their preference for soft drinks since it is the same price with the new product by Dr. Pepper Snapple group.

Hence, Dr. Pepper Snapple group  will need to have people with a desire for a beverage other than soda or water  for marketing to occur.  

6 0
3 years ago
Read 2 more answers
Hart Technology must accrue a loss contingency. The amount of the loss can be reasonably estimated within a range of outcomes. O
Shtirlitz [24]

The amount of loss that should be recognized is the <u>minimum amount </u><u>of the </u><u>range. </u>

<u />

<h3>Recording a Contingent liability </h3>
  • It should only be recorded if the loss is probable and the amount to be incurred as liability can be reasonably estimated.
  • If neither of the above are possible, the loss would be recorded as a footnote.

US GAAP rules state however that if the loss is probable and the amount is in a range, the amount to be recorded as a contingent liability should be the minimum of the range.

In conclusion, they should recognize the minimum amount.

Find out more on contingent liabilities at brainly.com/question/17371330.

3 0
2 years ago
Other questions:
  • A _____relationship would include your coworkers and friends
    10·2 answers
  • The difference between the ________ and the ________ from the sale of a product is called producer surplus.
    10·1 answer
  • A new customer, age 45, has been terminated from his assembly-line job of the past 20 years at an automotive parts supplier. Dur
    8·1 answer
  • Suppose that when the price of good X falls from $10 to $8, the quantity demanded of good Y rises from 20 units to 25 units. Usi
    13·1 answer
  • On October 10, Joleen Vora applied for a $50,000 life insurance policy with Magnum Life Insurance Co. She named her husband, Jay
    15·1 answer
  • Bravo Company began operations at the beginning of 20X6 with a $10,000 cash investment by stockholders. During 20X6, Bravo Compa
    12·1 answer
  • make price and output decisions without regard to what their competitors might do. have no perceptible influence on the market p
    14·1 answer
  • What will be the inventory Cost that was valued at 286000 valued at<br>.And obsolete cost is 8400​
    14·1 answer
  • A fund has a Beta of 1.25, Standard Deviation of 7%, and an expected return of 12%. If the risk free rate is 2%, calculate the T
    8·1 answer
  • Swifty Corporation is constructing a building. Construction began on January 1 and was completed on December 31. Expenditures we
    5·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!