D 3.1-12. Consider the following problem, where the value of c₁has not yet been ascertained.Maximize z = C₁x₁ + x₂,subject tox₁ + x₂ ≤ 6x₁ + 2x₂ = 10andX₁ ≥ 0, x₂ = 0.Use graphical analysis to determine the optimal solution(s) for(x₁, x₂) for the various possible values of c₁(-∞

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Answered: 3.1-12. Consider the following problem,…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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3. Suppose that a consumer has a utility function u(x1, x2) = x1 + x2. Initially the consumer faces prices (1, 2) and has income 10. If the prices change to (4, 2), calculate the compensating and equivalent variations. [Hint: find their initial optimal consumption of the two goods, and then after the price increase. Then show this graphically.] please do step by step and show the graph
i need the answer and steps to understand how
4. Zack consumes mangosteen(m) and chalta (c) and his satisfaction function from consumingthese fruits is given by S = (m+2)(y+1) The price of mangosteen Pm = 4 and the price of chalta, Pc = 6. He has 130 taka to spend on these fruits.a. Write the Lagrangian function.b. Find the optimal levels of purchase for mangosteen and chalta.c. Use bordered Hessian to prove that the second order condition is satisfied.d. What is the value of the Lagrangian multiplier? Show that if the budget is increased by one Taka,the increase in his satisfaction level is equal to the value of the Lagrangian multiplier.

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3.1-12. Consider the following problem, where the value of c₁ s not yet been ascertained. Maximize Z = C₁x₁ + x₂, pject to x₁ + x₂ ≤ 6 x₁ + 2x₂ = 10 d -₁ ≥ 0, x₂ = 0. e graphical analysis to determine the optimal solution(s) for for the various possible values of