Use Lagrange multipliers to find the maximum and minimum values of the function subject to the given constraints. (If an answer does not exist, enter DNE.) maximum minimum 27 2 Need Help? Read t X
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- Find maximum and minimum value by Lagrange multipliersFind the minimum value of f (x, y) = xy subject to the constraint 5x - y = 4 in two ways: using Lagrange multipliers and setting y = 5x -4 in f(x,y).A company plans to manufacture a rectangular box with a square base, an open top, and a volume of 452 cm3. The cost of the material for the base is 0.4 cents per square centimeter, and the cost of the material for the sides is 0.6 cents per square centimeter. Determine the dimensions of the box that will minimize the cost of manufacturing it. What is the minimum cost?
- Solve min x1-x2-2x3 problem by means of Lagrange multipliers under the constraints of x1+x2+x3=5 and x12+ x22 =4. Explain what the values of Lagrange multipliers mean?A rectangular box is going to be made with a volume of 274 cm3 . The base of the box will be a square and the top will be open. The cost of the material for the base is 0.3 cents per square centimeter, and the cost of the material for the sides is 0.1 cents per square centimeter. Determine the dimensions of the box that will minimize the cost of manufacturing it. What is the minimum cost?An open rectangular box with a square base of side-length "" is to be constructed out of two different materials. The base is made out of heavier material costing 25 per m ^ 2 , while the four sides are made out of lighter material costing $10 per m ^ 2 . Our goal is to create the cheapest possible box that has a volume of 10m ^ 3 Find an equation for the total cost of the box in terms of only Show work along with a suitable diagram. Then determine the global minimum of this equation and state the optimal dimensions for this box.
- Minimize ?=?+3?+10 subject to: 2?+4?≥8 4?+3?≥12 ?,?≥0 Corner points at _______________________ Minimum value of ___________ at x = __________ and y = __Use Lagrange multipliers to find the minimumvalue of the function f(x, y) = x2 + y2subject to the constraintxy = 3.Minimum:Formulate the objective function and the constraints for a situation in which a company seeksto minimize the total cost of materials A and B. The per pound cost of A is $25 and B, $10.The two materials are combined to form a product that must weigh 50 pounds. At least 20pounds of A and no more than 40 pounds of B can be used. Obtain the feasible region andsolution using graphical method.
- An open-top box is to have a square base and a volume of 10 m3. The cost per square meter ofmaterial is 5 dollars for the bottom and 2 dollars for the four sides. Let x and y be lengths of thebox’s width and height respectively. Let C be the total cost of material required to make the box.Find the dimensions of the box so that the cost of materials is minimized. What is this minimum cost?A cylinder-shaped can needs to be constructed to hold 600 cubic centimeters of soup. The material for the sides of the can cost 0.04 cents per square centimeter. The material for the top and bottom of the can need to be thicker and costs 0.05 cents per square centimeter. Find the dimensions for the can that will minimize production costs. Minimum cost:7. Use Lagrange multipliers to give an alternate solution. Find two positive numbers whose product is 100 and whose sum is a minimum.