Answered: min 4a1 + 5xз 2x1 + x2 – 53 -3x1…

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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(4) Ivan is laying out a page of a newspaper. He knows he needs to get 50 square inches of text on the page, and that the page must have 1 inch margins on the left and right side, a 2 inch margin at the top, and a 1 inch margin at the bottom. What is the minimum possible area of such a page?
(ii)For each set of the following total revenue and total cost functions, first express profit t as a function of output x and then determine the maximum level of profit by finding the vertex parabola(6) of the (а)TR — —6х? + 1200х, ТC 3D 180x + 3350 (b)TR -4 x? + 900x, TC = 140x + 6100
(2-T) ABC is a small manufacturer of two types of popular all-terrain snow skis, the J and the D models. The manufacturing process consists of two principal departments: fabrication and finishing. The fabrication department has 12 skilled workers, each of whom works 7 hours per day. The finishing department has 3 workers, who also work a 7-hour shift. Each pair of J skis require 3.5 labor hours in the fabricating department and 1 labor hour in finishing. The D model requires 4 labor hours in fabricating and 1.5 labor hours in finishing. The company operates 5 days a week. ABC makes a net profit of $50 on the J model and $65 on the D model. In anticipation of the next ski-sale season, ABC must plan its production of these two models. Because of the popularity of its products and limited production capacity, its products are in high demand, and ABC can sell all it can produce each season. The company anticipates selling at least twice as many D as J models. (Use Geogebra) Write your LP…
Sketch the following problem graphically: max f = x2 X2 subject to g1 = X1 – (1 – x2)³ < 0 92 = x1 2 0 Find the solution graphically. Apply the optimality conditions and monotonicity rules. Discuss. (From Kuhn & Tucker, 1951.)
Suppose the demand functions faced by the monopolist firm are as follows: Q1 = 40 -2P1 + P2 Q2 = 15 + P1 – P2 Whereas, the cost function is given as : C = Q21 +Q1Q2 +Q22 Find the Maximum level of profit and also identify the optimal level of P1 and P2.
Consider the following optimization problem: max x1 + 2x2 -x1 + x2 >= -4 x1 + x2 <= 15 - x1 + 3x2 <= 25 x2 >= 0 Graph the polyhedron corresponding to the set of feasible solutions of (P). Is the set of feasible solutions a polytope (bounded polyhedron)?
The following intermediate tableau for a dual maximum problem was obtained using the simplex method for optimizing a minimum problem. (see image) Perform all the necessary pivot and row operations to obtain the final tableau. Then, using the final tableau, answer the following questions: The minimum function value is: The value of x1 in the minimum problem is : The value of x2 in the minimum problem is:

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min 4a1 + 5xз 2x1 + x2 – 53 -3x1 subject to = 1 + 4x3 + x4 = 2 X; 2 0, i = 1, 2, 3, 4.