A rectangular storage tank with an open top is to have volume (20 m). Thelength of the base is twice the width, see the figure. The Material of the basecosts (20 $) per square meter. The material of the sides costs (10 $) persquare meter. Use Lagrange multiplier method to find the optimumdimensions of a tank that give the minimum cost.2wAns./ 1 3.914w x 1.957h = 2.61

Answered: Image /qna-images/answer/9175057c-4458-4ce7-b049-0a46d0a5e7e4.jpg

Answered: A rectangular storage tank with an open…

College Algebra (MindTap Course List)

12th Edition

ISBN:9781305652231

Author:R. David Gustafson, Jeff Hughes

Publisher:R. David Gustafson, Jeff Hughes

Chapter6: Linear Systems

Section6.8: Linear Programming

Problem 4SC: If the cost of each Robust tablet increases to 75 c and the cost of each Vigortab increases to 80 c...

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Similar questions

If the cost of each Robust tablet increases to 75 c and the cost of each Vigortab increases to 80 c , find the minimum cost.
In an open-top drawer, the material cost of the two sides is $240 per m2. The material cost of the back is $500 per m2. The material cost of the front and the bottom are $1000 per m2 and $100 per m2 respectively. Use the method of Lagrange multipliers to find the dimensions of the most economical drawer having a volume of 0.08m3.
A box without a lid is required to have volume, V = 32000 cm^3. Minimize theamount of cardboard required to create this box. Do NOT use Lagrange Multipliers.
Having 3m2 of aluminum foil at your disposal, you want to build a rectangular box with a lid, in such a way that it reaches the largest possible volume. Use Lagrange Multipliers to calculate the volume of this box.
A large container in the shape of a rectangular solid must have a volume of 480 m3. The bottom of the container costs $5/m2 to construct whereas the top and sides cost $3/ m2 to construct. Use Lagrange multipliers to find the dimensions of the container of this size that has the minimum cost.
A cardboard box without a lid is to have a volume of 32,000 cm3 . Find the dimensions that minimize the amount of cardboard used.
A rancher plans to use an existing stone wall and the side of a barn as a boundary for two adjacent rectangular corrals. Fencing for the perimeter costs 10 per foot. To separate the corrals, a fence that costs 8 per foot will divide the region. The total area of the two corrals is to be 7,000 square feet. Use Lagrange multipliers to find the dimensions that will minimize the cost of the fencing.
A silo is to be built with a vertical cylindrical tube with no bottom but topped by a hemispherical dome. The silo must have a volume of 32πm3. The dome material costs $8/m2 and the tube material costs $3/m2. Find the dimensions of the silo that minimize the cost.
A microwaveable cup-of-soup package needs to be constructed in the shape of cylinder to hold 400 cubic centimeters of soup. The sides and bottom of the container will be made of styrofoam costing 0.02 cents per square centimeter. The top will be made of glued paper, costing 0.07 cents per square centimeter. Find the dimensions for the package that will minimize production cost. Radius: ? cmHeight: ? cmMinimum cost: ? cents
A trapezoidal gutter is to be made from a sheet of tin 22 cm wide by ending up the edges. If the base is 14 cm wide, what width across gives top gives the greatest carrying capacity? (APPLICATION OF MAXIMA AND MINIMA)
A box with a square base and open top must have a volume of4000cm^3. Find the dimensions of the box that minimize the amount of material used.
a) Amran is constructing a rectangular box with a square base and an open top. The box must havea volume of 42592 cm3. If Amran wants to minimize the amount of material used, what shouldthe dimensions of the box be?

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