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
posledela
3 years ago
11

STAR Co. provides paper to smaller companies whose volumes are not large enough to warrant dealing directly with the paper mill.

STAR receives 100-feet-wide paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The demands for these widths vary from week to week. The following cutting patterns have been established: Number of:Pattern 12ft. 15ft. 30ft. Trim Loss1 0 6 0 10 ft.2 0 0 2 10 ft.3 7 0 0 4 ft.4 1 2 2 1 ft.5 7 1 0 1 ft.Trim loss is the leftover paper from a pattern (for example, for pattern 4, 1(12) + 2(15) + 2(30) = 99 feet used resulting in 100-99 = 1 foot of trim loss). Demands this week are 5,672 12-foot rolls, 1,67015-foot rolls, and 3,200 30-foot rolls. Develop an all-integer model that will determine how many 100-foot rolls to cut into each of the five patterns in order to meet demand and minimize trim loss
Mathematics
1 answer:
mamaluj [8]3 years ago
3 0

Answer:

  see below

Step-by-step explanation:

In order for the problem to make sense, we have to assume typos in Patterns 2, 3, and 4. We suppose they should be (0, 0, 3, 10), (8, 0, 0, 4) and (2, 1, 2, 1).

If we let p, q, r, s, t represent the number of rolls cut to patterns 1 to 5, respectively, then we want ...

  minimize 10p +10q +4r +s +t . . . . . . . total trim loss

  subject to ...

     0p +0q +8r +2s +7t = 5672 . . . . . . number of 12-ft rolls

     6p +0q +0r +1s +1t = 1670 . . . . . . . . number of 15-ft rolls

     0p +3q +0r +2s +0t = 3200 . . . . . . number of 30-ft rolls

     p≥0, q≥0, r≥0, s≥0, t≥0

_____

The solution works out to be (p, q, r, s, t) = (1, 0, 253, 1600, 64) with a trim loss of 2686 feet (equivalent to 27 100-ft rolls).

Note that we have endeavored to fill the order exactly. We don't know if there are cut choices that would minimize loss further, but result in a few rolls extra of some width or another.

You might be interested in
15 pounds of ham to make 35 sandwiches. How much ham per sandwich?
polet [3.4K]
15 pounds / 35 sandwiches ~ 0.43 pounds ham per sandwich
3 0
2 years ago
Let v be an eigenvector of a matrix A with a corresponding eigenvalue ?=2. Find one solution x of the system Ax=v.
Murljashka [212]

Answer with explanation:

For, a Matrix A , having eigenvector 'v' has eigenvalue =2

 The order of matrix is not given.

It has one eigenvalue it means it is of order , 1×1.

→A=[a]

Determinant [a-k I]=0, where k is eigenvalue of the given matrix.

It is given that,

k=2

For, k=2, the matrix [a-2 I] will become singular,that is

→ Determinant |a-2 I|=0

→I=[1]

→a=2

Let , v be the corresponding eigenvector of the given eigenvalue.

→[a-I] v=0

→[2-1] v=[0]

→[v]=[0]

→v=0

Now, corresponding eigenvector(v), when eigenvalue is 2 =0

 We have to find solution of the system

→Ax=v

→[2] x=0

→[2 x] =[0]

→x=0, is one solution of the system.

5 0
3 years ago
What is the total surface area of rectangular prism?
algol13

Answer:

162 [m²].

Step-by-step explanation:

required surface is:

A=(3*7+6*7+3*6)*2=162 [m²].

4 0
2 years ago
Read 2 more answers
Find the zeros of the function F(x)=x^2-9x-9
Marta_Voda [28]
F(x)=x^3+x^2-9x-9
x^2(x+1)-9(x+1)
=(x+1)(x^2-9)

=(x+1)(x+3)(x-3)
Hope that this helps
8 0
3 years ago
Simplify each expression completely.<br>7[3+2(x-4)-6(x-4)]
sergeinik [125]

Answer:

21 + 14x - 56 - 42x + 168

= 133  - 28x

Step-by-step explanation:

6 0
3 years ago
Read 2 more answers
Other questions:
  • Help please thank you
    5·2 answers
  • Need help please! Answer ASAP please!!
    11·2 answers
  • Sanjay graphs a quadratic function that has x-intercepts of –3 and 7. Which functions could he have graphed? Check all that appl
    7·2 answers
  • If two variables were completely correlated, their correlation coefficient would be:
    10·1 answer
  • Formulate a system of equations that could be solved by multiplying one equation by 5 and then adding the two equations together
    7·1 answer
  • To solve the problem below, you must write a clear and convincing justification for accepting one of the possible answer choices
    12·1 answer
  • HELP, WILL GIVE BRAINLIEST!!
    9·1 answer
  • Please help with this math question
    15·1 answer
  • Question 6
    9·1 answer
  • Quadrilateral ABCD is dilated by a scale factor of 2 centered around (2,2).
    6·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!