Determine two positive numbers e and f whose product is 27 and for which the value of 4f +3e is a minimum.

Q: The minimum value of the function f(x, y) = (x – 1)² + (y – 1)² subject to the constriant x? + y² =…

A: To find the minimum value of the function f(x,y)=(x-1)2+(y-1)2 subject to constraint x2+y2=8. Let,…

Q: Given the functionP(x) = x – 2x +0+ A + 12 where and A are unknown 2nd and 1st order terms. The…

A: given function P(x)=x5-2x3+□+∆+12where □ and ∆ are unknown 2nd and 1st order terms.we have to find…

Q: Find the minimum value of g(t)=t3−588t+4 on the interval [−7,15]

A: We can find the minimum value as below

Q: If a and b are positive numbers, find the maximum value of f(x)= xa(9 − x)b on the interval 0 ≤ x ≤…

A: To find the maximum value of f(x)

Q: For æ = 4 the function f(x) = x? + bx +c has the minimum value of -9. Fine

A: The given function is f(x)=x2+bx+c has a minimum value = -9 at x = 4.

Q: Find the relative maximum and minimum values. =x2 + y² - 6x + 12y - 9

A:

Q: 5. y2 2x y26-x fx, y) = 4x+ 3y Minimum: Maximum: | | | | |

A: We need to find maximum and minimum values of f(x,y).

Q: h(z) = x² - 16z + 60? What is the minimum value of

A: First method: Given: hx=x2-16x+60 Add and subtract 64 from h(x) to complete the square. Therefore,…

Q: Among all pairs of numbers (x,y) such that 4x+2y=18 find the pair for which the sum of squares,…

A: Given  4x+2y=18 y=18-4x2=9-2x f=x2+y2 Put the value of y in f f=x2+9-2x2f=x2+81+4x2-36x  =5x2-36x+81

Q: The total revenue (in hundreds of dollars) from the sale of x X-ray machines and y bone density…

A: Given: Rx,y=15+169x+182y-5x2-7y2-7xy

Q: If a and b are positive numbers, find the maximum value of f(x) = xa(5 − x)b on the interval 0 ≤ x ≤…

A:

Q: Please

A:

Q: For what value of x the function x2+y2 is minimum if x+y=20

A:

Q: Find the minimum value of xy, when p²x* + q²y* = r². %3D

A:

Q: Find the area of a triangle bounded by the y axis, the line f(x)=9−2/5x, and the line perpendicular…

A: fx=9-25x Comparing with fx=mx+c, we get m=slope=-25c=y-intercept=9 Therefore the slope of a line…

Q: Find the minimum value of the function g(t) = t2 - 6t + 9, 1 … t … 6.

A:

Q: Suppose that x and y are two positive numbers, and suppose that r+ 2y = 30. Find the maximum value…

A: Given that: x+2y=30…

Q: A manufacturer of lighting fixtures has daily production costs of C= 800 - 50x + 0.25x?, where C is…

A:

Q: Find the relative maximum and minimum values. f(x.y)= 8xy-x - 4y

A: Given :f(x,y)=8xy-x3-4y2

Q: Find the maximum of Q= xy if x+ y = 50. The maximum value of Q is Q =

A:

Q: For each value of λ the function h(x,y)=x2+y2−λ(6x+4y−18) has a minimum value m(λ). For which value…

A:

Q: Find the absolute minimum value of the function f (x, y) = 2x² + 2y? subject to the constraint 9x2 +…

A:

Q: Q1. The sum of three positive numbers is 30, find the three numbers if their product is minimum?

A: Topic- Number System

Q: The population density of a city is given by P(x,y) = - 25x - 30y + 500x + 240y + 180, where x and y…

A: Population density is given by following function  P(x, y) = - 25x2 - 30y2 +500x + 240y + 180

Q: Find the relative maxima or minima. Maximum of ƒ(x, y) = 12xy - x2 - 3y2, subject to x + y = 16

A: f(x,y)=12xy-x2-3y2 , subject to x+y=16

Q: What is the minimum of the function y = -a + 3x for a <-1? %3D -4 -2 04 O2

A:

Q: For what value of X does the function f(x) = x³ – 9x² – 120x+6 have a relative minimum? A 10 В) 4 3

A: f(x)=x3-9x2-120x+6

Q: Among all pairs of numbers (x,y)such that 4x+2y=22 , find the pair for which the sum of squares,…

A:

Q: z = x? + xy + y² - y

A:

Q: Find the minimum and maximum of y = f(x) = x³ – x² – 3x + 2

A:

Q: the maximum value M and the minimum value m of f(x,y) =x^3-2y^2 subject to the constraine…

A: According to question given that f(x,y)=x3-2y2Subject to constrainex3+y3=125

Q: For what value of X does the function f(x) = x³ – 9x² – 120x+6 have a relative minimum? (A) 10 (в) 4

A: solution is given below .

Q: Find the maximum profit and the number of units that must be produced and sold in order to yield the…

A:

Q: Total revenue for manufacturing x running shoes and y basketball shoes is given by…

A:

Q: The degree of f(x) is [odd and the leading coefficient is negativev. There are real zeros and…

A: Consider the graph

Q: Find three positive numbers x, y, and z whose sum is 21 and product is a maximum.

A: There are two different questions in the image. According to our guidelines, we can solve only one…

Q: Draw the graph of f ( x ) =3 x2+5 x−4 for a. From the graph, identify the values of x when f (x)=0.…

A: Follow the steps below to plot the graph of y=f(x) . Take arbitrary integers for the values of x…

Q: Of all numbers whose difference is 4, fınd the two that have the minimum product. x= y=

A: Given that  Difference of two number is 4 and we need to find the two numbers whose product is…

Q: Suppose that x and y are two positive numbers, and suppose that x + 2y = 30. Find the maximum value…

A: Given data:   The first equation is x+2y=30. The expression for the function is f(x,y)=(x+1)(y+3).…

Q: nd two numbers whose sum is 24 with the condition that the sum of the square of one plus six es the…

A: Topic:- calculus

Q: Find two positive numbers x and y such thatx + 2y 50 and (x + 1)(y+ 2) is a maximum.

A:

Q: Find the relative maximum and minimum values. f(x,y) = x² +y2 +4x- 12y

A:

Q: Find the absolute maximum value and absolute minimum value of f(x, y) = 2a2 + 2y² + 4y – 1 on the…

A:

Q: Find the number of units, x, that produces the maximum profit P, if C(x) = 45+4x and p = 60 - 2x. A.…

A:

Q: Please

A:

Q: The population density of a city is given by P(x,y) = - 20x - 20y + 560x + 440y + 200, where x and y…

A:

Q: Please

A:

Q: The function f(x) =px²-qx+ 32, p 0 has a minimum value of 0 when x= 4. Find the value of p and of q.…

A: The given function is f(x)=px2-qx+32. To use the minima information of the function, let us…

Q: Find the absolute minimum value of the function 3x? + 2y? subject to the constraint f(x, y) 4.x2 +…

A:

Q: Find the relative maximum or minimum value (if any) of f(x, y) = 2x3 + xy2 + 5x2 + y2

A: The given function is: f(x,y)=2x3+xy2+5x2+y2