Using Lagrange multipliers Find the maximum area of a right triangle whose perimeter is 4. Note: Using Lagrange multipliers Note 2: include all the steps that are carried out to arrive at the result

Q: An isosceles triangle is inscribed in a circle of radius R. Find the value of 0 that maximizes the…

A: In this question we have to find which option is good.

Q: Optimization An open-top rectangular box is to have a square base and a surface area of 100 cm2.…

A: Given: Surface area of an open top rectangular box = 100 cm2. To find: We have to find the…

Q: A rectangular frame must have a perimeter of 60 cm. What dimensions should the frame have to…

A: let the dimension of the rectangular frame be x (length) and y (breadth)

Q: Use Lagrange multipliers to solve the given optimization problem. Find the maximum value of f(x, y)…

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Q: Use Lagrange multipliers to solve the given optimization problem. Find the minimum value of f(x, y)…

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Q: Optimal garden A rectangular flower garden with an area of30 m2 is surrounded by a grass border 1 m…

A: Consider the length of the flower is L and width is W. Then To minimize the combined area of garden…

Q: BONUS: Use Lagrange multipliers to find the dimensions of the box with largest volume possible and…

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Q: Use Lagrange multipliers to solve the given optimization problem. Find the maximum value of f(x, y)…

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Q: A rectangular storage tank with an open top is to have volume (20 m). The length of the base is…

A: Given that:

Q: Use the Lagrange multipliers approach and determine the optimized perimeter of the following shape…

A: According to the given information, it is required to determine the value of b in inches for the…

Q: 5) Using Lagrange multipliers, find the maximum value of z =x + 2y subject to the constraint that x2…

A: For a function f(x) which is to be maximized subjected to the constrains g(x,y)=0, and taking λ as…

Q: A A cone-shaped drinking cup is made from a circular piece of paper of radius R by cutting out a…

A: It can be only half filled and hence a cup can have maximum capacity of volume of semi sphere, which…

Q: Minimum Cost An industrial tank of the shape described in Exercise 33 must have a volume of 4000…

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Q: You are making a rectangular box with a square base and an open top. Its volume must be 4 ft^3. Find…

A: Let the length of a side of the base= x Height = y So, volume= x2y=4  Or, y=4/x2   Surface area:…

Q: 20. Minimizing surface area. Drum Tight Containers is designing an open-top, square-based,…

A: Volume of a cuboid is lbh. Since it is mentioned that it is square-based so l=b. l2h=62.5 in3…

Q: 7. A Norman window has the outline of a semicircle on top of a rectangle, as shown in the figure.…

A: The available wood trim is 8+π. The window the of the shapes semi-circle and rectangle.

Q: Aylindrical can has a volume of 167 cm³. Use Lagrange multipliers to determine the dimensions of the…

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Q: You must show all work to receive full credit. 1. In order to ship a box through the US Postal…

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Q: A box without a lid is required to have volume, V = 32000 cm^3. Minimize the amount of cardboard…

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Q: 10. rectangular box with a square base and open top must have a volume of 4 m³. Find the dimensions…

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Q: A rectanglular box without a front and without a bottom is to be built. The volume of the box equals…

A: The objective of the question is to determine the dimensions of the cuboid, with the minimum…

Q: 10.) volume of 480 ft'. The bottom will cost $5 per square foot to construct and the sides and top…

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Q: 21. Minimizing surface area. An oil drum of standard size has a volume of 200 gal, or 27 ft³. What…

A: Let the radius of the drum be rft and height be hft. As the volume of the drum is 27ft We get…

Q: A covered box is to be made from a rectangular sheet of cardboard measuring 10 inches by 16 inches.…

A: Volume of the box=x.y.z —1                                   height*lenth*width    2x+z=10  —2…

Q: سؤال ثاني/ A rectangular storage tank with an open top is to have volume (20 m³). The length of the…

A: By using langrange multiplier method

Q: Use Lagrange multipliers to find the dimensions of a rectangular box of maximum volume such that the…

A: Use Lagrange multiplier to solve.

Q: A rectangular storage tank with an open top is to have volume (20 m). The length of the base is…

A: Given that the volume of the container is 20m3 i.e. Volume = 20 m3 Material cost of base = $20 m2…

Q: 1. Using Lagrange multipliers, find three positive numbers whose sum is 18 and such that the sum of…

A: The Lagrange multipliers method is a strategy for finding local maxima or minima of a function using…

Q: Oil from an offshore rig located 5 miles from the shoreline is to be pumped to a location on the…

A: The situation is illustrated as shown in the figure below: Here, the objective is to find the…

Q: A cardboard box without a lid is to have a volume of 16,384 cm³. Find the dimensions that minimize…

A: Volume of the cardboard =16,384 cubic cm let x= length of side of the box, h= height of the box y=…

Q: A closed rectangular bOX with a volume of 16ft° is made from two kinds of materials. The top and…

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Q: A satellite dish is the shape of a paraboloid. The dish is 30 inches wide, and 10 inches deep. How…

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Q: box with a square base and open top must have a volume of 13,500 cm3. Find the dimensions of the box…

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Q: Minimizing Packaging Costs If an open box has a square base and a volume of  (180 in.^3) and is…

A: Now,         Let,length = width =xHeight =y.Now,V=108x2y=108y=108x2   ............1

Q: APPLICATION: 1. A pigpen is to be enclosed using 640 m of fencing along three of its sides, the…

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Q: Use Lagrange multipliers to solve the given optimization problem. Find the minimum value of f(x, y)…

A: Rewrite the problem with the constraint in the form gx,y=0. Minimize fx,y=x2+y2 subject to xy2=16.…

Q: A closed rectangular box with a volume of 375ft is made from two kinds of materials. The top and…

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Q: 10. You have a load of tiles that can cover an area of 400 t. You want to cover a rectangular shape…

A: From the given equations  P=2x+2(400/x) P=2x+(800/x) P'(x)=2-(800/x2)=0 x=20

Q: Numerical Method Design the optimal cylindrical container that is open at one end and has walls…

A: Given that volume V=0.2 m3. We know that the volume of the cylinder is V=πr2h. ⇒h=Vπr2 And the…

Q: Use Lagrange multipliers to solve the given optimization problem. Find the maximum value of f(x, y,…

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Q: A closed rectangular box witha volume of 16ft is made from two kinds of materials. The top and…

A: A closed rectangular box with a volume of 16 ft3 is made from two kinds of materials. The top and…

Q: A farmer has 800 feet of fencing with which to build a holding pin with a cattle shoot at one end as…

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Q: 2. A 27-in gutter is bent on two sides as shown. Find the r and o values that will maximize the area…

A: From the given diagram:The cross-sectional area…

Q: A closed rectangular box with a volume of 1715ft' is made from two kinds of materials. The top and…

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Q: Rectangular boxes with a volume of 8 m³ are to be made of three materials. The material for the top…

A: Let the dimensions of the box be x,y, and z. Given the volume of the rectangular box is xyz=8. Let…

Q: You are designing a glass candle holder.  It will be a rectangular prism with outer surface area 200…

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Q: A nursery school wants to build a fence around the playground outback of three equal sections. The…

A: Consider the fig. for the playground to find the length and width for the playground.

Q: A closed rectangular box with a volume of 2187ft' is made from two kinds of materials. The top and…

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Q: (Optimization) A closed cylindrical storage drum is to be made with a volume of 16 ft3. What are the…

A: Given:- (Optimization) A closed cylindrical storage drum is to be made with a volume of 16 ft3. To…