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
yuradex [85]
3 years ago
10

The following is a linear programming formulation of a labor planning problem. There are four overlapping shifts, and management

must decide how many employees to schedule to start work on each shift. The objective is to minimize the total number of employees required while the constraints stipulate how many employees are required at each time of day. The variables X1 - X4 represent the number of employees starting work on each shift (shift 1 through shift 4).
MIN X1 + X2 + X3 + X4

s.t. X1 + X4 ≥ 12 ........(on duty during shift 1)
X1 + X2 ≥ 15 ........(on duty during shift 2)
X2 + X3 ≥ 16 ........(on duty during shift 3)
X3 + X4 ≥ 14 ........(on duty during shift 4)
X1, X2, X3, and X4 ≥ 0

Given the optimal solution: X1* = 13, X2* = 2, X3* = 14, X4* = 0, how many workers would be assigned to shift 2?

a. 13
b. 12
c. 14
d. 15
e. 2
Mathematics
1 answer:
dexar [7]3 years ago
6 0

Answer:

d. 15

Step-by-step explanation:

Putting the values in the shift 2 function

X1 + X2 ≥ 15

where x1=  13, and x2=2

13+12≥ 15

15≥ 15

At least 15 workers must be assigned to the shift 2.

The LP model questions require that the constraints are satisfied.

The constraint for the shift 2 is that the  number of workers must be equal or greater than 15

This can be solved using other constraint functions e.g

Putting  X4= 0 in

X1 + X4 ≥ 12

gives

X1 ≥ 12

Now Putting the value X1 ≥ 12  in shift 2 constraint

X1 + X2 ≥ 15

12+ 2≥ 15

14 ≥ 15

this does not satisfy the condition so this is wrong.

Now from

X2 + X3 ≥ 16

Putting X3= 14

X2 + 14 ≥ 16

gives

X2  ≥ 2

Putting these in the shift 2

X1 + X2 ≥ 15

13+2 ≥ 15

15 ≥ 15

Which gives the same result as above.

You might be interested in
Which of the following are the zeroes of the function y = 3 ( x − a )( x + b )y = 3 ( x - a )( x + b ) in terms of a a and bb ?
Murljashka [212]
I believe the answer is <span> bb</span>
8 0
3 years ago
Read 2 more answers
1.48 as a fraction ​
Leni [432]

Answer:

148/100=37/25

Step-by-step explanation:

Who have to think how many zeros it took for the decimal to get between the 1 and 4.

148/100=37/25 is your answer.

4 0
3 years ago
Read 2 more answers
Which matrix represents the system of equations shown below? 3x-5y=12 4x-2y=15
tatuchka [14]

Answer:

\left[\begin{array}{ccc}3&-5  &|12\\4&-2  &|15\\\end{array}\right]

Step-by-step explanation:

When making a matrix of two equations with the variables x and y, the result will be a matrix with three columns:

  • a column for the values of x in each equation
  • a column for the values of y in each equation
  • a column for the independent values of each equation

since our system of equations is:

3x-5y=12\\ 4x-2y=15

we can see that the value for x in the first equation is 3 and in the second equation is 4, thus the first column will have the numbers 3 and 4:

\left[\begin{array}{ccc}3&&\\4&&\\\end{array}\right]

Now for the values of y we hvae -5 in the first equation and -2 in the second equation, we update the matrix with another column with the values of -5 and -2:

\left[\begin{array}{ccc}3&-5&\\4&-2&\\\end{array}\right]

Finally, the last column is the independent values of each equation (or the results) in the first equation that number is 12 and in the second equation is 15, thus the matrix is:

\left[\begin{array}{ccc}3&-5&12\\4&-2&15\\\end{array}\right]

usually there is a line separating the columns for the values of x and y, and the independent values:

\left[\begin{array}{ccc}3&-5  &|12\\4&-2  &|15\\\end{array}\right]

this is the matrix of the system of equations

6 0
3 years ago
Find the area and perimeter of triangle ABF with F(-3,0), A(1,3), and B(7,-5)
lions [1.4K]

Answer:

Step-by-step explanation:

The area would be 25 square centimeter

8 0
3 years ago
Help plz I really need some help right now
Montano1993 [528]
1/2 chance of getting an even number and 1/2 chance of getting an odd one.
8 0
3 years ago
Read 2 more answers
Other questions:
  • Mr. Torres took his students to the dolphin show. Each row in the stadium had 9 seats. One adult sat at each end of a row, and e
    9·1 answer
  • How do I make 105 over 8 a mixed number
    9·1 answer
  • Lyra and Donna are testing the two-way radios they built for their high school science project. Lyra goes to the top of a buildi
    10·2 answers
  • If there are 12 eggs in a carton, how many are in 5 cartons?
    14·2 answers
  • Which function has a range of y &lt; 3?<br> y=3(2)*<br> y=2(3)<br> y=-(2)*+ 3<br> O y=(2]*_3
    13·1 answer
  • A girl has a square pool with an area of 81 square feet and she adds a patio which is 3 feet wide around the pool what is the to
    5·1 answer
  • What is the minimum number of degrees that a regular hexagon can be rotated before it carries onto itself?
    13·2 answers
  • Need help in the b question... Pls send it fast.. urgent and if possible do it in paper and send or just type it.. need answer f
    13·1 answer
  • Find the volume of this sphere. Use 3.14 for pi and round your answer to the nearest 10th.
    5·2 answers
  • 2. Which is NOT in the fact family for<br> 3, 4, and 12?<br> 6. N<br> fo<br> ir
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!