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
notsponge [240]
3 years ago
9

The Springer Dog Food Company makes dry dog food from two ingredients. The two ingredients (A and B) provide different amounts o

f protein and vitamins. Ingredient A provides 16 units of protein and 4 units of vitamins per pound. Ingredient B provides 8 units of protein and 8 units of vitamins per pound. Ingredients A and B cost $0.50 and $0.20 per pound, respectively. The company wants its dog food to contain at least 12 units of protein and 6 units of vitamins per pound and be as inexpensive as possible.
a. Reformulate an LP model for this probelm

b. Sketch the feasible region for this problem

c. Determine the optimal solution to the problem by enumerating the corner points.

d. How will the optimal solution change if the company requires only 5 units of vitamins per pound rather than 6?

Mathematics
1 answer:
Nataly [62]3 years ago
3 0

Answer:

a) Objective function (minimize cost):

C=0.50A+0.20B

Restrictions

Proteins per pound: 16A+8B\leq 12

Vitamins per pound: 4A+8B\leq 6

Non-negative values: A,B\geq0

b) Attached

c) The optimum solution (minimum cost) is 0 pounds of ingredient A and 0.75 pounds of ingredient B. The cost is $0.15 per ration.

d) The optimum solution changes. The cost is now 0 pounds of ingredient A and 0.625 pounds of ingredient B. The cost is $0.125 per ration.

Step-by-step explanation:

a) The LP formulation for this problem is:

Objective function (minimize cost):

C=0.50A+0.20B

Restrictions

Proteins per pound: 16A+8B\leq 12

Vitamins per pound: 4A+8B\leq 6

Non-negative values: A,B\geq0

b) The feasible region is attached.

c) We have 3 corner points. In one of them lies the optimal solution.

Corner A=0 B=0.75

C=0.50*0+0.20*0.75=0.15

Corner A=0.5 B=0.5

C=0.50*0.5+0.20*0.5=0.35

Corner A=0.75 B=0

C=0.50*0.75+0.20*0=0.375

The optimum solution (minimum cost) is 0 pounds of ingredient A and 0.75 pounds of ingredient B. The cost is $0.15 per ration.

d) If the company requires only 5 units of vitamins per pound rather than 6, one of the restrictions change.

The feasible region changes two of its three corners:

Corner A=0 B=0.625

C=0.50*0+0.20*0.625=0.125

Corner A=0.583 B=0.333

C=0.50*0.583+0.20*0.333=0.358

Corner A=0.75 B=0

C=0.50*0.75+0.20*0=0.375

The optimum solution changes. The cost is now 0 pounds of ingredient A and 0.625 pounds of ingredient B. The cost is $0.125 per ration.

You might be interested in
12 eggs cost $2.04. How much would 18 cost ?
Salsk061 [2.6K]
The answer to this sum is 
$8.04
4 0
3 years ago
Read 2 more answers
Name the missing coordinate(s) of each triangle
Cloud [144]

Answer:

13) C (a, a)  Y (a, 0)

14) B (0, b)  P (a, 0)

Step-by-step explanation:

13) Y lies on x axis so it is Y(a,0)

ZY = YC = a

so for C coordinates are (ZY,YC) = (a, a)

14) B lies on y axis so it is B(0, b)

BK = BP = \sqrt{a^{2} + b^{2}  } = distance between two points

so P is (a, 0) as it is same distance and on positive side of x axis

3 0
2 years ago
Read 2 more answers
Jacob distributed a survey to his fellow students asking them how many hours they'd spent playing sports in the past day. He als
andrew-mc [135]

Answer:8.75

Step-by-step explanation:

4 0
2 years ago
Read 2 more answers
Will give 15 points and brainliest
pentagon [3]

Answer:

 1331π cm³

Explanation:

\sf V_{cylinder} = \pi (radius)^2 (height)

Here given:

  • radius: 11 cm
  • height: 11 cm

Hence find volume:

\sf \rightarrow\pi (11)^2 (11)

\sf \rightarrow 121\pi ( (11)

\sf \rightarrow 1331\pi \quad \approx \:\:\ 4181.46 \ cm^3

4 0
1 year ago
Read 2 more answers
I need help plzzzzzz
eduard
The answer is 3.7a+3b

Because you combine like terms
3 0
2 years ago
Read 2 more answers
Other questions:
  • Salma bought 3 CDs that were each the same price. Including sales tax, she paid a total of $44.70. Of that total, $2.10 was the
    8·1 answer
  • The expression 6x^2-3x-4 has ___ terms and a constant of ____.
    10·1 answer
  • Find the sum of 67.008 and 3.8
    12·1 answer
  • The sum of two numbers is 64. Twice the smaller number is 10 less than the larger number. What are the numbers?
    15·2 answers
  • Express 0.7 as a fraction
    15·2 answers
  • What is the simplified form of the quantity of x plus 5, all over 2 + the quantity of x plus 6, all over 2?
    15·1 answer
  • Suppose the chance of winning a game is 1/50. If you play the game 50 times independently, is it certain that you will win? If n
    8·1 answer
  • the slope of a graphed line is 5 and the y-intercept is (0,3/4), what is the slope-intercept equation of the line?
    7·1 answer
  • Went out of town for a family emergence and don't know how to do this????
    13·1 answer
  • WILL MARK BRAINLIEST <br> Which of the following is not true?
    7·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!