MATHEMATICS COLLEGE

Use the technique developed in this section to solve the minimization problem. Minimize C = −3x − 2y − z subject to −x + 2y − z ≤ 20 x − 2y + 2z ≤ 25 2x + 4y − 3z ≤ 30 x ≥ 0, y ≥ 0, z ≥ 0 The minimum is C = at (x, y, z) = .

Answers

Answer 1
Answer:

Answer:

C= -145, (35/4, 295/8, 45)

Step-by-step explanation:

Use Gaussian elimination to find the values of x, y and z

Eq 1: -x+2y-z=20

Eq 2: x-2y+2z=25

Eq 3: 2x+4y-3z=30

  • Multily Eq1 by 1 and add to Eq 2

Eq 1: (-x+2y-z=20 ) × 1

Eq 2:  x-2y+2z=25

Eq 3:  2x+4y-3z=30

⇒ Eq1: -x+2y-z=20

    Eq2:         z= 45

   Eq 3: 2x+4y-3z=30

  • Multiply Eq 1 by 2 and then add to Eq 3

Eq1:  (-x+2y-z=20 ) × 2

Eq2:            z= 45

Eq3:   2x+4y-3z=30

⇒ Eq1:  -x+2y-z=20

   Eq2:            z= 45

  Eq3:      8y-5z= 70

  • swap Eq 2 and Eq 3

Eq 1: -x+2y-z=20

Eq 3:     8y-5z= 70

Eq 2:       z= 45

  • Solve Eq 2 for z

Z=45

  • solve Eq Eq 3 for y.

y= 295/8

  • Using the value z=45 and y= 295/8, substitue in Eq 1 to get value of x

x= 35/4

  • Substitue values of x,y and z in C= -3x-2y-z to get minimum value of C

C= -145

Related Questions

In a particular class of 31 students, 14 are men. What fraction of the students in the class are men?
A pool in the shape of a rectangular prism is 6 meters long and 3 meters wide. the water in the pool is 1 meter deep.a. the density of water is about 1 gram per cubic centimeter. find the number of kilograms of water in the pool. question 2b. you add 6000 kilograms of water to the pool. what is the depth of the water in the pool? write your answer as a fraction. the water is about meters deep.
State whether the following function is a linear function f(x)=x-4
Anyone got the answer to this? Ik it’s prob easy but I’m just not seeing it
Find the product of these complex numbers.(8 + 5)(-7 + 9) = A. -101 +37i B.-11-107/ C. -11 +37/ D. -101-107/

At what x-values do the graphs of the functions y = cos 2x and y =3cos^2x-sin^2x intersect over the interval -pi

Answers

To find:

The x-values at the intersection of the graphs of two functions.

Solution:

Two functions are:

y=\cos2x\text{ and }y=3\cos^2x-\sin^2x

The functions are equal at the intersection. So,

\cos2x=3\cos^2x-\sin^2x

The solutions of the above equation are the x-values of the intersection.

\begin{gathered} \cos2x=3\cos^2x-\sin^2x \n \cos^2x-\sin^2x=3\cos^2x-\sin^2x \n 2\cos^2x=0 \n \cos^2x=0 \n \cos x=0 \end{gathered}

The solution to the above equation is:

x=(\pi)/(2)+2\pi n\text{ and }x=(3\pi)/(2)+2\pi n

It is given that x lies between -pi and pi. So, the value of n = 0 for the first solution and n = 1 for the second solution. Therefore,

x=(\pi)/(2)\text{ and }x=-(\pi)/(2)

Thus, options A and B are correct.

Multiply. Write your answer in simplest form.
-√2(-2+√5)

Answers

Step-by-step explanation:

this is all I can find I hope it helps you out us not I'm sorry

suppose that you made four measurement of a speed of a rocket: 12.7 km/s, 13.4 km/s, 12.6 km, and 13.3 km/s. compute: the mean, the standard deviations, and the standard deviation of the mean

Answers

Answer:

Mean = 13 kilometer per second

Standard Deviation = 0.4082 kilometer per second

Step-by-step explanation:

We are given the following data set of rocket speed in kilometer per second in the question:

12.7, 13.4, 12.6, 13.3

Formula:

\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}  

where x_i are data points, \bar{x} is the mean and n is the number of observations.  

Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}

Mean =\displaystyle(52)/(4) = 13

Deviations from mean = -0.3, 0.4, -0.4, 0.3

Sum of squares of differences =

0.09 + 0.16 + 0.16 + 0.09 = 0.5

S.D = \sqrt{(0.5)/(3)} = 0.4082

Mean = 13 kilometer per second

Standard Deviation = 0.4082 kilometer per second

16. The original price of a tie is $12.50. The new price of the tie is now$7.50. By what percentage was the tie marked down? *

Answers

The tie was marked down by 40%

Mrs. Smith is giving a homework pass to a student whose expression is equivalent to - i. Which expression will win the homework pass?A. i^36
B. i^37
C. i^38
D. i^39
Help pleaseee

Answers

Answer:

D. i^39

Step-by-step explanation:

If you simplify i^39, you get i^35, i^31, i^27, i^23, i^19, i^15, i^11, i^7, to i^3, which is equal to -i.

How do you do this question?

Answers

Step-by-step explanation:

K is an upper bound for│f"(x)│on the interval [0, 1], so x ≤ 1.

Sine and cosine have maximums of 1, so an upper bound of │f"(x)│is:

│f"(x)│≤ (76 · 1 + 152 · 1 · 1)

│f"(x)│≤ 228
Other Questions
Which graphs represent functions?
What is the greatest common factor of 18, 36 , and 54
An architect needs to consider the pitch, or steepness, of a roof in order to ensure precipitation runoff. The graph below showsthe vertical height, y, versus the horizontal distance, x, as measured from the roof peak's support beam. Roof Steepness y 14 12 10 8 Vertical Height (feet) 4 2 +X 10 12 14 0 2 4 6 8 Horizontal Distance (feet) Determine the equation that could be used to represent this situation.
The ratio of cats to dogs at the shelter is 3 to 2 if there are 15 cats at the shelter how many dogs are there