f(x1,x2)420-2-4−1201102-1X13-2x2Figure 2: Graph of the function f(x1, x2) = 2x1 = x²-x+3Consider the following function:f(x1, x2) = 2x1 - x-x+3.-For your visual convenience, a portion of the function is depicted in Figure 2.(a) Compute the gradient vector of f.(b) Compute the Hessian matrix of f.(c) Determine all points that yield stationary values of f.(d) Use the second-order conditions to determine whether each of the stationary val-ues of f is a maximum, a minimum, or neither.

The objective of the question is to compute the gradient vector, the Hessian matrix, find the…

Answered: f(x1,x2) 4 2 0 -2 -4 −1 2 0 1 1 0 2 -1…

ENGR.ECONOMIC ANALYSIS

14th Edition

ISBN:9780190931919

Author:NEWNAN

Publisher:NEWNAN

Chapter1: Making Economics Decisions

Section: Chapter Questions

Problem 1QTC

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Determine the total area under the standard normal curve in parts (a) through (c) below. (a) Find the area under the normal curve to the left of z = - 1 plus the area under the normal curve to the right of z = 1. The combined area is 03173 (Round to four decimal places as needed.) (b) Find the area under the normal curve to the left of z = – 1.55 plus the area under the normal curve to the right of z=2.55. The combined area is (Round to four decimal places as needed.)
Suppose you have a linear optimization model where you are trying to decide which products to produceto maximize profit. Answer the following questions and be as specific as possible.(a) What does the additive assumption imply about the profit objective? (b) What does the proportionality assumption imply about the profit objective? (c) Can you think of any reasonable profit functions that would not be linear in the amounts of theproducts produced?
The Augsburg math club paid $200 for fancy souvenir water bottles that they are going to sell next year for $6 each at the Taste of Augsburg during Homecoming Weekend. Define two variables that relate quantities in this story. Which one is the input of this function and which one is the output? Write an equation for your function, and briefly explain why your function is valid.
Consider the following figure. 6 tr yield per acre (tonnes) 4 2 B C | A 10 20 30 40 50 60 70 fertilizer applied per acre of wheat This non-linear function shows that over the range shown, 80
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Let S represent the amount of steel produced (in tons). Steel production is related to the amount of labor used (4) and the amount of capital used (C) by the following function. S- 20100.70 In this formula L represents the units of labor input and C the units of capital input. Each unit of labor costs $50, and each unit of capital costs $100. (a) Formulate an optimization problem that will determine how much labor and capital are needed in order to produce 55,000 tons of steel at minimum cost. Min s.t. -55,000 L.C20 (b) Solve the optimization problem you formulated in part (a). (Hnt: When using Excel Solver, start with an initial L>O and Co. Round your answers to the nearest integer.) at (L. C) =
2. (This problem derives the general result that any polynomial function is of a lower asymptotic order than any exponential function.) First, we prove a special case. Suppose that we have two functions, f(n) = n² and g(n) = 2". We will prove that f(n) = O(g(n)). • port (a). (c) Show that, for any n ≥ no, it must be the case that f(n) ≤ cog(n) = f(n+1) ≤ cog(n+1). Precisely state the argument by induction that n² = 0(2¹). Now, define f(n) = nk where k ≥ 1, g(n) = a", where a ≥ 1. (d) (Slightly harder). Argue that, for any k and a, there exists some n₁ such that : (1₁+¹)* < a.
2. (This problem derives the general result that any polynomial function is of a lower asymptotic order than any exponential function.) First, we prove a special case. Suppose that we have two functions, f(n) = n² and g(n) = 2". We will prove that f(n) = O(g(n)). (e) (Slightly harder) Find a constant c₁ such that f(ni) ≤ cig(n1), where n₁ is defined as in part (d). (f) (Harder) Show that, for any n ≥ n₁, it must be the case that f(n) ≤ cig(n) ⇒ f(n+1) ≤ cig(n+1), and therefore nk = O(a") for all k, a ≥ 1.
I need the answer as soon as possible
1 1 a) Let A = 1 -1 -1 1 (i) Compute the value of det (A). (ii) For what values of x will the matrix be singular? b) Write down the quadratic form that corresponds to the following matrix. 2 4 2 -1 -3 .4 -3 1
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