Use Lagrange Multipliers to find the volume of the largest open-top box that has 120 m^2 of surface area, and 70 m of edge length (sum of all edges)
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- Use the method of Lagrange multiplier to determine the absolute maximum and min-imum values of the function subject to the given constraint.Pls. show complete solution and right answer. Thanks.A rectangular vault is to be constructed on an existing floor at a bank so as to enclose avolume of 485 cubic meters. The cost per square meter of materials is $2,000 for the ceiling,$9,000 for the wall with the door and $3,000 for the other three walls. The minimized costof the vault rounded to the nearest $1,000 dollars is:a. $964,000b. $971,000c. $982,000d. $993,000Use the "big M method" (i.e., alternative variables and Ma1 variables) to solve for this maximization problem with mixed constraints. Show all work.
- Use the method of Lagrange multiplier to determine the absolute maximum and minimum values of the function subject to the given constraint.Find maximum and minimum value by Lagrange multipliersIn order to ensure optimal health (and thus accurate test results), a lab technician needs to feed the rabbits a daily diet containing a minimum of 24 grams (g) of fat, 36 g of carbohydrates, and 4 g of protein. But the rabbits should be fed no more than five ounces of food a day.Rather than order rabbit food that is custom‐blended, it is cheaper to order Food X and Food Y, and blend them for an optimal mix. Food X contains 8 g of fat, 12 g of carbohydrates, and 2 g of protein per ounce, and costs $0.20 per ounce. Food Y contains 12 g of fat, 12 g of carbohydrates, and 1 g of protein per ounce, at a cost of $0.30 per ounce. What is the optimal blend? a. Choose the unknowns, i.e. variables. Statewhat they are so you know exactly whatyou are looking for.b. Write your OPTIMIZATION EQUATION. c. Write the constraints as a system ofinequalities, usually there are several.d. Graph the system and identify thefeasibility region. e. Identify the corners of the feasibilityregion, which will be…
- In order to ensure optimal health (and thus accurate test results), a lab technician needs to feed the rabbits a daily diet containing a minimum of 24 grams (g) of fat, 36 g of carbohydrates, and 4 g of protein. But the rabbits should be fed no more than five ounces of food a day.Rather than order rabbit food that is custom-blended, it is cheaper to order Food X and Food Y, and blend them for an optimal mix. Food X contains 8 g of fat, 12 g of carbohydrates, and 2 g of protein per ounce, and costs $0.20 per ounce. Food Y contains 12 g of fat, 12 g of carbohydrates, and 1 g of protein per ounce, at a cost of $0.30 per ounce. What is the optimal blend?Please give a clear and detailed solution. Use Lagrange multipliers to find the maximum and minimum values of this function subject to the constraint.Use Lagrange multipliers to find three positive numbers whose sum is 230 and whose product is maximum.
- 7. Use Lagrange multipliers to give an alternate solution. Find two positive numbers whose product is 100 and whose sum is a minimum.use lagrange multipliers to find the largest and smallest values of -y^2 + 2xy - 2x^2 with constraint of x^2 + y^2 <= 1A closed rectangular box with a square base and a volume of 12 cubic feet is to be constructed from two different types of materials. The top is made of a metal costing $2 per square foot and the remainder of wood costing $1 per square foot. Find the dimensions of the box for which the cost of materials is minimized.