13 #10) As the operator of the Abba Company, you determine the price and cost functions tomaximum the profit of x units are a product are given by p = 600 – 3x2 and C =600 + 6x - 0.3x2. How many units of this product must be produced to maximum theprofit and what is the maximum profit?#11) Chocolate Box Company is going to make open-topped boxes out of a 6-inch x 16-inchrectangle piece of cardboard by cutting squats out of the corners and folding up the sides.What are the dimensions of the box in order to have the largest volume? What is the volume?# 12) Company XYZ has established the price for a given commodity x is given by the equationp = 200 – x. If it cost $100 to make each of these commodities and $1000 for which runthe plant, find the maximum profit.# 13) Find two positive numbers x and y for which 2x + y = 30 such that xy2 is maximized.# 14) A fence must be built in a large field to enclose a rectangular area of 20,000 ft2.Fencing material cost $ 2.50 per foot for the two sides facing north and south and $3.20 perfoot for the other two sides. Find the cost of the least expensive fence.

Answered: Image /qna-images/answer/2594fd42-92ae-4c1b-8462-8828053e3b20.jpg

Answered: # 13) Find two positive numbers x and y…

Math

Calculus

# 13) Find two positive numbers x and y for which 2x +y = 30 such that xy² is maximized.

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter9: Systems Of Equations And Inequalities

Section: Chapter Questions

Problem 13T

See similar textbooks

Related questions

Q: X~N(22,3) find maximum of x in bottom quartile

Q: Suppose that f(x, y) = x² − xy + y² − 5x + 5y with x² + y² ≤ 25. 1. Absolute minimum of f(x, y) is…

Q: Find the maximum value of z = xy2 subject to 2x2 + y2 = 294; x ≥ 0, y ≥ 0. z =

A: Given information : z = xy2 subject to 2x2 + y2 = 294; x≥0; y≥0.

Q: 16. Of all points (x, y, z) that satisfy 3x + 4y + 2z = 52, find the one that minimizes (x – 1)2 +…

A: Let f(x,y,z)=x−12+y−42+z−22 and g(x,y,z)=3x+4y+2z−52≡0Apply Lagrange Multiplier method to find…

Q: ! Find the max/min point for z = f(x, y) =-5x² -10y² + 20x+ 20y.

Q: If f'(x) = x - 2x-x +2, thenf has a relative minimum at x= -2 O0 0 O0

Q: Maximize Q = xy, where x and y are positive numbers such that x+3y 16. The maximum value of Q is and…

A: Maximize Q=xy, where x and y are positive numbers such that x+3y2=16

Q: Find positive numbers x and y, whose sum is 75, such that xy2 is maximized.

A: Positive numbers x and y,x+y=75xy2 is maximized

Q: Find the number in the interval [ – 1, - 0.25] so that the sum of that number and its square is…

Q: Suppose that f(z, y) – e ¯4r² - 4y² - z + 2y Then the maximum is

A: The given function is: f(x,y)=e-4x2-4y2-x+2y Here,…

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

A: To solve the following problem

Q: Find two nonnegative numbers x and y with 2x + y = 3 for which the term xy² is maximized. by

A: Given 2x+y=30, we need to maximize xy2

Q: Find two nonnegative numbers x and y for which 2x + y = 30, such that xy2 is maximized.

A: Given that, 2x + y= 30 y = 30 - 2x ................... (1) The function is: f(x, y) = xy2 f(x) = x…

Q: Maximize z= 4x +3y エ+5y S 25 4x + y < 24 Subject to Maximum is Preview at Preview Preview VI VI ALAI…

A: Draw the given constraints to find the feasible area.

Q: Maximize Subject to Maximum is X = y = z = 2x + y x + 5y < 4x + 5y ≤ X Y 25 40 νι νι ΛΙ ΛΙ 00 at

Q: Maximize z = x + 3y 3x +7y > 63 54 at

Q: Find two positive numbers x and y that minimize the product xy, and satisfyx + 4y = 120.

Q: Find the local minimum value of f(x, y) = 4+ xl+yl1 11æy. -

Q: Find positive numbers x and y such that x + y = 48 and 5x2y + 10 is maximized.

A: Given that, x + y= 48 y = 48 - x ................... (1) The function is: f(x, y) = 5x2 y+ 10 f(x) =…

Q: Suppose that x and y are two positive real numbers so that x + y = 10. Maximize the product xy

A: To find the solution of the given problem use the second derivative test. Second derivative test:…

Q: Find the quadratic function f (x) = ax2 + bx + c that goes through (0, 1) and has a local minimum at…

A: Given: The quadratic function fx=ax2+bx+cpasses through the point 0,1 and has local minimum at 1,-1,…

Q: Minimize g=10x+9y Subject to 4x+y≥19 2x+y≥13 x+4y≥24 x≥0 y≥0 What is the minimum value and at…

Q: Maximize: z =x+ 10y subject to: 6x+ 5y < 30 10x +ys 30 X20, y 2 0 The maximum value is

A: Constraints: 6x+5y≤3010x+y≤30 Graph each inequality by finding x and y intercepts 6x+5y=30x…

Q: 1. Find the maximum value of f(x, y) = 4xy where x > 0 and y > 0, subject to the constraint 9. = 1.

Q: Maximize F=x+y subject to: x+2y≤8 x≤6 x, y ≥0 Corner points at ____________________ Maximum…

A: We have to find maximum.

Q: Find the minimum values of the function (x, y) = x² + 2y² that lic on the cirele x² + y² =1

A: Given : Function fx,y = x2 + 2y2 Circle x2 + y2 = 1 To find : Minimum values of the given…

Q: What value of b >-1 maximizes f(b) = J - x) dx!

Q: Use the two-stage method to solve. Find x, 20 and x, 20 such that X1 + 2x2 s 22 X1 + 3x2 2 12 2x, +…

A: In Two Stage Method, the whole procedure of solving a linear programming problem (LPP) involving…

Q: Find the absolute maximum and minimum values of the function on the triangular region whose vertices…

A: The given function f(x, y) is a polynomial and therefore, it is continuous and has both maximum and…

Q: Find all points (x,y) where f(x.y) has a possible relative maximum or minimum. f(x.y) = x* - 32xy +…

A: Solution:Given thatfx,y=x4 -32xy+8y2-10we have to find all points x,y where fx,y has a possible…

Q: Find the minimum value ofx +y +z² given x+y+z=3a.

Q: Of all points (x,y,z) that satisfy x+y+4z=24, find one that maximizes (x-1)2 +(y-1)2+(z-1)2

Q: Find the maximum and minimum values of the function f(x, y, z) = 3x - y - 3z subject to the…

Q: Find the maximum value of f(x,y) = 13 – x -y on the line x+ 2y = 5.

Q: Determine the critical point and its type of function f with f (x, y) = 3x^2y + y^3 − 3x^2 − 3y^2 +…

Q: Solve the optimization problem. Maximize P = xyz with x +z = 18 and y +z = 18, and x, y, and z 2 0.…

A: NOTE: Refresh your page if you can't see any equations. . the first constraint is . the second…

Q: maximize f(x,y)=xy subject to the contraint 6x+y=18 the last question is what is the maximum valye…

A: max . fx,y=xyS.t 6x+y = 18 6x+y=18⇒ 6x+y-18=0∴ gx,y=6x+y-18=0 Fx,y,L=fx,y-L g x,y⇒…

Q: maximize 2= 1.8x, t H,2X2 Subgect to: 2.8X + 3.4x2= 21 1.4x1 +2.2x2 s 11 w+し ×、=o,メ2 Mo what is the…

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: Q#2: Maximize U=w°+z0.6 subject to 2w+4z=100 and find optimal value of x and z. Also, verify that…

Q: Maximize B = xy“, where x and y are positive numbers such that x + y = 3. The maximum value of B is

A: To maximize, B=xy2 --(1)Given that x+y2=3 ⇒y2=3-x substituting in (1)

Q: Maximize P = xyz with x +y = 12 and z+y = 12, and x¸ y, and z >0.

Q: Q1/Use simplex method to maximize the function max R=7x+ 4y Subjected to 2x+ y =20 X+Y< 18

A: To maximize R=7x+4y S.T.C. 2x+y=20x+y≤18x≤8 Introduce the slack and artificial variables: Max…

Q: The demand for face masks is given by p =-3 In(x) + 10 with domain [1, 28] where x is the number of…

A: Given: The demand for face masks is given by, p=-3 lnx+10, with domain 1, 28 where x is the number…

Q: = 1 Find the minimum value of f(x, y, z) = 3x − y − 3z subject to x² + 2z² - - and x + y -z = 0.

Q: Find two numbers x and y with x-y = 20 for which the term xy is minimized.

A: In this problem, we have to find the two numbers "x and y"

Q: Find the number in the interval [ – 1, - 0.25] so that the sum of that number and its square is…

Q: Minimize f(x,y)=x2-y2 subject to the contraint 3x-7y=-4 when the minimum occurs, what is a. x?…

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

Question

#10) As the operator of the Abba Company, you determine the price and cost functions to
maximum the profit of x units are a product are given by p = 600 – 3x2 and C =
600 + 6x - 0.3x2. How many units of this product must be produced to maximum the
profit and what is the maximum profit?
#11) Chocolate Box Company is going to make open-topped boxes out of a 6-inch x 16-inch
rectangle piece of cardboard by cutting squats out of the corners and folding up the sides.
What are the dimensions of the box in order to have the largest volume? What is the volume?
# 12) Company XYZ has established the price for a given commodity x is given by the equation
p = 200 – x. If it cost $100 to make each of these commodities and $1000 for which run
the plant, find the maximum profit.
# 13) Find two positive numbers x and y for which 2x + y = 30 such that xy2 is maximized.
# 14) A fence must be built in a large field to enclose a rectangular area of 20,000 ft2.
Fencing material cost $ 2.50 per foot for the two sides facing north and south and $3.20 per
foot for the other two sides. Find the cost of the least expensive fence.

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

This is a popular solution!

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Trending now

This is a popular solution!

Step by step

Solved in 3 steps with 3 images

SEE SOLUTION Check out a sample Q&A here