Letter C only please 10. Find the global maximizers and minimizers, if they exist, for the following functions: (a) f(x1, X2) = xỉ – 4x, + 2x3 + 7. (b) f(x1, x2) = e-(*}+x})' (c) f(x1, x2) = xỉ – 2x, x2 + }x} – 4x2. (d) f(x1, X2, x3) = (2x1 – x2)? + (x2 – x3)² + (x3 – 1)?. (e) f(x1, X2) = x + 16x1x2 + x.

Q: Is the point a = [0, 1]T a local minimizer? %3D

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Q: A piece of wire of length L is to be cut into two pieces, one piece to form a square and the other…

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Q: Find two numbers such that their difference is 5 and their product is minimum.

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Q: A farmer wants to fence an area of 13.5 million square feet in a rectangular field and then divide…

A: Let one side be length P and the other QTotal area = PQ =13.5 million

Q: 2. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the…

A: Product of two positive number is 750. The sum of one and 10 times of another is minimum.

Q: A manufacturer has determined that the total cost C of operating a factory is C = 2.5x2 + 75x +…

A: Given  Cx = 2.5x2+75x+25000

Q: A rectangular lot is to be fenced in using two different kinds of fencing. Three sides will be…

A: Given that, Three sides of rectangular land will be fenced using standard fencing that costs $7 per…

Q: Use Lagrange multipliers to find three positive numbers whose sum is 18 and the sum of whose squares…

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Q: Suppose a corporation manufactures candles at two locations. The cost of producing *1units at…

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Q: Suppose that a company has received an order for 200 units of its product and wishes to distribute…

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Q: 1. The sum of two positive numbers is 200. What is the maximum possible value for their product? 2.…

A: As question number is not mentioned in the given attachment. So, I am solving first question. Kindly…

Q: The marginal cost of a company is MC = 100 – 20x + x². 2006 and the fixed cost is The quantity that…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: we want to build a box with a square base and an open top and the box will enclose 108 cubic inches.…

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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: A manufacturer's total cost equation per day is given by the equation TC = 440+4q+,00010². If each…

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Q: Find the number in the interval [ - 5,5] so that the sum of six times the number and its square is…

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Q: Suppose that a company needs 5 x 10,000 items during a year and that preparation costs are $5 for…

A: Given that: Demand (D) = 50,000 Cost per unit(C) = $3 Order quantity(Q) = x Cost of preparation(S) =…

Q: Find the point on the graph of y = 1x that is closest to the point (2, 0). [Hint: 2(x - 2)2 + y2 has…

A: Given: y=x Let the point closest to (2,0) be P(x,y). Distance between point P(x,y) and (2,0) is:…

Q: Let æ and y be positive numbers such that a+y 21. Find the values of x and y that minimize 3x +y.…

A: We will solve the given problem using Lagrange Multiplier Method.

Q: The production function for a firm is p(x, y) = 68x"y"", where x and y are the number of units of…

A: By Method of Lagrange's multiplier . To maximize fx,y,z subject to gx,y,z=k  Solve system of…

Q: A manufacturer's total cost equation per day is given by the equation TC = 440 + 4q +,0001Q². If…

A: Given: TC=440+4q+0001Q2 To find: Solution

Q: Suppose a corporation manufactures candles at two locations. The cost of producing *1units at…

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Q: A rectangular lot is to be fenced in using two different kinds of fencing. Three sides will be…

A:

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: Find two positive numbers x and y that maximize Q = x2y if x + y = 2.

A: Given function - Q = x2y               ...........(1)And,x+y = 2y = 2-x…

Q: Forwarded Maximize z = 2x1 + 3x2 subject to 5x1 + 7x2 \leq35 4x1 + 9x2 \leq36 x1, x2 \geq 0 and…

A: Maximization of a linear programming problem is carried out to obtain a solution that follows all…

Q: Use the duality method to solve each linear programmin 1. Minimize Z = 29x,+ 10x2 subject to: 3x,+…

A: Given that  Minimum z=29x1+10x2subject to 3x1+2x2≥2                   5x1+x2≥3…

Q: 1. Find non-negative numbers x and y such that x + y = 150 and ²y is maximized. 2. You are to…

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Q: 1. Without using Lagrange Multipliers, find three positive numbers whose sum is 100 and whose…

A: let the numbers be "x" and "y" Given the sum of numbers is 100  then  x+y=100                  Then…

Q: Suppose the labor cost (in dollars) for manufacturing a particular product can be approximated by…

A: Given that the labor cost is approximated by the function Lx,y=32x2+y2-8x-6y-2xy+197.Here x is…

Q: piece of wire is with a length of 4 m is cut into two pieces, and the resulting two pieces are…

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Q: 9. The difference of two numbers is 30. What two numbers will minimize the prod- uct?

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Q: roduction function for a firm is p(x, y) = 96xy", where x and y are the number of units of labor and…

A: According  to guidelines  we solve one question. Thanku

Q: A piece of wire of length 67 is cut, and the resulting two pieces are formed to make a circle and a…

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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

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Q: A rock formation is 3 miles due north of its closest point along a straight shoreline. A visitor is…

A: Given A rock formation is 3 miles due north of its closest point along a straight shoreline. A…

Q: The marginal cost of a company is MC = 100 – 20x + x², 2006 and the fixed cost is 3 The quantity…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: A hiker finds himself in a forest 4 miles directly east of the nearest point along a road that runes…

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Q: A satellite television reception station is to be located at point P so that the sum of the squares…

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Q: Suppose the labor cost (in dollars) for manufacturing a camera can be approximated by  L(x,y)=…

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Q: Since the feasible region is closed and bounded, we know that the maximum value will occur at…

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Q: Use Lagrange multipliers to find three positive numbers whose sum is 230 and whose product is…

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Q: A boat in the ocean is 3 miles from the nearest point on a straight shoreline; that point is 5 miles…

A: Given- A boat in the ocean is 3 miles from the nearest point on a straight shoreline; that point is…

Q: A boat is located 3 km in the ocean from a point, says P on a straight shoreline. That point is 5 km…

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Q: Of all numbers whose sum is 54​, find the two that have the maximum product. That​ is, maximize…

A: we have to find the value of x and y when Q has maximum value. the solution is following.

Q: A piece of wire of length 60 is cut, and the resulting two pieces are formed to make a circle and…

A: Let x be the length of the wire cut for the circle then the length of the wire cut for the square.If…

Q: What necessary conditions are replaced by "minimize"? obeyed by a solution to (1) if "maximize" were

A: To write the  necessary condition for min ∫t0t1F(t,x(t),x'(t))dt with x(t0)=x0

Q: Suppose the labor cost (in dollars) for manufacturing a camera can be approximated by L(x.y) =x +y -…

A: Given: Suppose the labor cost in dollars for manufacturing a camera can be approximated by Lx,…

Q: A river flows between the lines x = 3 and x = 4. Where should a bridgebe constructed to minimize the…

A: A river flows between the line x=3 and x=4. Bridge constructed to the path from O(0,0) to P(5,4).

Limits of Multivariable Functions

Multivariable calculus is an extension of single variable calculus. It involves several variables instead of just one. Assume there is an open set containing points (x0, y0), let f be a function defined in that open interval except for the points (x0, y0). The multivariable limit of this function as it approaches the points (x0, y0) and is denoted as: