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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10. Find the value of P which minimizes the following function (and the value of Y at the minimum). a. Y= 30 + Q – 10Q. b. Y= 50 +0.5Q² – 7.5Q.
5. Company A plans to market a new product. The marketing department has determined that the demand for these products is p = - 0.05x + 620,0sx< 30,000, where p denotes the product's unit price (in dollars) and x denotes the quantity demanded. Also, the company estimates that the total cost (in dollars) incurred in manufacturing x products per year of production will be C(x) = 100x +710,000. Find the marginal revenue function and the marginal profit function.
4a. State if the following are True or False The constant k in y k = - is called constant of proportionality. If k> 1, the graph of function f(kx) is horizontally stretched. A linear function model passes through every point of a data set. Hence the model will perfectly forecast unknown function values When the function is decreasing as the input value increases, the graph of the function is always concave up. If a > 0, then the parabola opens down. 4b. A homeowner wants to enclose a portion of the backyard for a rectangular garden as shown below garden The garden is fenced off on two of its sides. If the homeowner has 70 feet of fencing, write the equation for the area, A, of the garden in terms of its width, w. bes
4. The demand for face masks is given by p =- 3 In(x) + 10 with domain [1, 28] where x is the number of face masks (in thousands) that can be sold at a price of Sp. How should the face masks be priced in order to maximize the reveniue?
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

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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