3. Find three positive integers x, y, and z if their sum is 30 and the sum of the square is a minimum.

Q: The minimum value of J.y,Z) = 6x - y – óZ subject to the constraints *+y -Z=0 and ? + 2? = 1 is?

A: Given,          The minimum value of fx,y,z=6x-y-6z subject to the constraints x+y-z=0 and x2+2z2=1.

Q: Find maximum and minumum values of f(x, y, z) = 8x – 16y + 40z subject to the constraint x2 + y² +…

A: The explanation of answer as follows :-

Q: Find the minìmum and maximum values of the function subject to the given constraint. (If an answer…

A: Given:- f(x, y) =8x+7y Constraint  x2+y2=4

Q: 1. Match the following: а. (h,k) AOS b. x=h Maximum/Minimum С. а Vertex d. y= k Opening

A:

Q: Solve the problem. 10) Maximize Q = xy2, where x and y are positive numbers, such that x + y2 = 5.

A:

Q: li'm, n are positive integers and the equations x² + mx + 2n = 0 and x² + nx + m = 0 have real rots.…

A: According to question, Given quadratic equation,x2 + mx +2n =0,andx2 + nx +  m = 0,above  quadratic…

Q: Find the minimal solution of x+2y-z = 1; 2x+3y+z = 2; 4x+7y-z = 4.

A: Given:

Q: Find maximum and minumum values of f(x, y, z) = 9x – 18y +45z subject to the constraint x? + y² + z²…

A:

Q: Find the minimum value of f(x,y)=66x2+9y2 subject to the constraint x2+y2-784

A:

Q: Consider the LP problem below: Max P= 5x + 6y Subject to: 4x+2y =0 Which of the following is not a…

A: Graphical method is used to solve linear programming problem involving two variables while linear…

Q: 3. Find the absolute maximum and minimum values of f(x, y) = x²y subject to the constraint x2 + y? =…

A: f(x,y)=x2y Constraint is:  g(x,y)=x2+y2-1

Q: Find the values of​ x, y, and z that maximize xyz subject to the constraint 192−x−8y−16z=0.…

A: Use the lagrangian's multiplier  xyz+λ192-x-8y-16z Partially differentiate with respect to x, y, z…

Q: Find the extremum of​ f(x,y) subject to the given​ constraint, and state whether it is a maximum or…

A: To find the extremum of fx,y=59-x2-y2 to the given constraint x+7y=50

Q: Find maximum and minumum values of f(x, y, z) = 3x – 6y + 15z subject to the constraint x2 + y? + z2…

A:

Q: Find maximum and minumum values of f(x, y, z) = 7x – 14y + 35z subject to the constraint x² + y? +…

A:

Q: , Find the minimum value of the function f(T, Y, z) = x² +y +z subject to the constraints a +…

A: To find the minimum value of the below function subject to constraints x + 4y + 6z = 2 and x + 7y +…

Q: Suppose two numbers x, y satisfy x – y = 4. The minimum value of the quantity x² + 3y? is O 24 12 36

A: Given  x-y =4 Then x=y+4 And minimum value of u=x2+ 3y2   ...(1)

Q: Find maximum and minumum values of f(x, y, z) = 8x – 16y + 40z subject to the constraint x? + y? +…

A: The given function is; f(x,y,z) = 8x-16y+40z

Q: Suppose that Isabella has 80 hours per week to allocate between work and leisure and she earns $10…

A: Let us take the total number of working hours as H and leisure hours as L.  Then L+H = 80, H = 80-L…

Q: Maximize z = x1+ r2 subject to ri + 2x2 0

A:

Q: 6 Find the minimum of –x + 2y on the feasible set given by x 2 0, x5 4, y 2 2, and x+y24. a) 0 b) 2…

A: We graph x≥0, x≤4, y≥2 and x+y≥4 using a graphing calculator.

Q: Find maximum and minumum values of f(x, y, z) = 5x – 10y + 25z subject to the constraint x2 + y? +…

A: we use Lagrange multipliers method

Q: Find the optimal solution. MAX Z=6X+7Y st 4X+5Y≤20 10X+7Y≤35 3X+4Y≥6 X ≥0 , Y ≥0 and an…

A:

Q: Find maximum and minumum values of f(x, Y, z) = 8x – 16y +40z subject to constraint x2 + y? + z2 =…

A:

Q: What is the minimum value of f(x, y) =x +4y -2x+8y subject to the constraint X+2y=7

A:

Q: 1. Find the maximum value of the function P(x,y) = 3x + 2y subject to the constraints x + 2y 0, and…

A: The function, Px,y=3x+2y subject to constraints x+2y≤4, x-y≤1, x≥0, and y≥0.

Q: 1 Consider two nonnegative numbers x and y such that x+y= 10 . Maximize and minimize y -

A: To find two non negative numbers x and y.

Q: Find the extreme values of f(x, y) = 12x + 3y, subject to the constraints xy = 4, x > 0, and y > 0.…

A: Solve the following

Q: Find the extremum of​ f(x,y) subject to the given​ constraint, and state whether it is a maximum or…

A: Given f(x,y)=xy and  11x+y=12 Apply the method of Lagrange Multipliers to calculate the extremum…

Q: What is the minimum value of f(x, y) =x +4y - 2x +8y subject to the constraint X+2y D7 O a. 5 O b.…

A: Use Lagrange multiplier to solve

Q: Find r and h that minimize S subject to the constraint V = 54n.

A: Here V=54π and we should minimize  S=2πrh+2πr2 under the constraint V=54π=πr2h V(r,h)=πr2h-54π

Q: Find the maximum of the following function: h(x,y) = In(x56 yl4) given the constraints: 4x2 + y? =…

A:

Q: Find the extremum of f(x.y) subject to the given constraint, and state whether it is a maximum or a…

A: The given function is, fx,y,z=x2+y2+z2 Consider another function g(x) from the constraint equation,…

Q: A wire 12 inches long is cut into two, one part is bent in the form of a circle, and the other into…

A: ANS: C

Q: Find the optimal solution. MAX   Z=6X+7Y st 4X+5Y≤20 10X+7Y≤35 3X+4Y≥6  X ≥0, Y ≥0 and X must not…

A: The graph of the given region is the following. Given that X must not be an integer and Y must be…

Q: QUESTION 15 Calculate the minimum value of 3x + 6y subject to the following constraints: x+y22 x +…

A: Given: A LPP, Min z=3x+6ysubject to,x+y≥2x+2y≤5x+y≤6x, y≥0 To find: Solution of given LPP.

Q: 12. Solve the following LP problem graphically by enumerating the corner points. МАX: 10X, + 12X2…

A:

Q: Find the minimum value of f subject to the given constraint. f(xy) = 3x +y -4xy; x+y= 24

A:

Q: If x and y are two positive numbers that satisfy xy = 7, then what is the minimum value of 2 x +3 y…

A: Find the minimum

Q: #3: Find the maximum of the following function: h(x, y) = In(x40 y8) given the constraints: 5x² + y²…

A:

Q: Find the minimum value of the function z = 3x+11y subject to the following constraints. x<11 ys 12…

A: Given, min z=3x+11ySubject to the constraintsx≤11y≤123x+y≥183x+7y≥54

Q: Find the absolute maxımum and minimum of f(r, y) = x² + y subject to the constraint 3x2 + 4y? = 5

A: To find the absolute maximum and minimum values of f(x,y) subject to constraint g(x,y).

Q: 24- Since D is a square whose vertices have coordinates (0,0), (0.2), (2,0), and (2.2), which of the…

A:

Q: Find the value of x and y which satisfy 2x + 3y = 8 and whose product is a minimum. a. 1 and 2…

A: we have to find

Q: Find the absolute maxluum of fr.4)=2y bject to the Constraint gixy)= x?ty²=/

A:

Q: 10. Let f(x, y) = x²y + y. Find the minimum and maximum values of f subject to the constraint x² +…

A: Given: fx,y=x2y+y The constraint equation is: gx,y=x2+y2=5   Now apply the Lagrange's multiplier;…

Q: Find the maximum and minimum values (if such values exist) of f(x, y) = x² + 6y² subject to the…

A:

Q: A wire 12 inches long is cut into two, one part is bent in the form of a circle, and the other into…

A:

Q: Find the maximum value of P = x + 6y subject to the following constraints: (2x +4y < 10 X+9y < 12 x…

A:

Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.