2. Consider the following set of constraints:X, + 2x, + 2x, + 4x, < 402x, - x, + x, + 2x, < 84x, – 2x, + x, – x,< 104.Using the Simplex Method, solve the problem for each of the following objectivefunctions.а. Маximize z 3 Зх, — х, + 3x, + 4x,b. Minimize z %3D 5х, - 4х, + 6х, — 8х,

(a) After introducing slack variables we have Max Z = 3x1-x2+3x3+4x4+0S1+0S2+0S3subjected…

Answered: 2. Consider the following set of…

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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Calculate the minimum value of 8x + 6y subject to the following constraints: x + y ≥ 23 x + 2y ≥ 27 2x + y ≥ 27 x ≥ 0 y≥0
A store store is looking to stock the following: necklaces, bracelets, rings, and earrings. The objective function measuring profit and constraints are given below. Constraint 1 measures display space in units, constraint 2 measurestime to set up the display in minutes. Constraints 3 and 4 are marketing restrictions. Setup an LP program in Tab "#1" and run additional reports (leave reports in your file) in order to answer the following questions.MAX 100X1+120X2+150X3+125X4S.T.1) X1+2X2+2X3+2X4<1082) 3X1+5X2+X4<1203) X1+X3<254) X2+X3+X4>50a. How many necklaces should be stocked?b. Now many bracelets should be stocked?c. How many rings should be stocked?d. How many earrings should be stocked?e. How much space will be left unused?f. How much time will be used?g. By how much will the second marketing restriction be exceeded?h. What is the profit?i. To what value can the profit on necklaces drop before the solution would change?j. By how much can the profit on rings increase…
1. Use the following situation to answer each question. a. Jules is in the business of constructing dog houses. A small dog house requires 8 square feet (ft²) of plywood and 6ft² of insulation. A large dog house requires 16ft2 of plywood and 3ft² of insulation. Jules has available only 48ft2 of plywood and 18ft2 of insolation. Write the constraints on the number of small (x) and large (y) dog houses that he can build with the available supplies and graph the solution set to the system of constraints. 1. Determine the Constraints (there are 4) 2. Graph the Constraints 3. Identify each vertex on the graph 4. A small dog house sells for $15 and a large dog house sells for $20, then how many dog houses of each type should be built to maximize the revenue to satisfy the constraints? a. Determine the linear function in two variables for the situation above. b. Using the vertices, determine the how many dog houses of each type should be built to maximize the revenue to satisfy the…
A decision problem has the following three constraints: 37X + 23Y <= 851; 19X + 21Y= 399; and 19X - Y <= 0.90476227 . The objective function is Min 3X + 33Y . The objective function value is : a. 0 b. unbounded c. 1200.2856 d. infeasible e. 600.14282
Prime Paints manufactures two types of paints, one for interior painting and the other for exterior painting. Both types require the use of two raw materials - M1 and M2, so that the maximum daily availabilities of these materials are 24 tons and 6 tons, respectively. It is known that 1 ton of the interior type of paint requires 4 tons of M1 and 2 tons of M2. On the other hand, 1 ton of the exterior type of paint requires 6 tons of M1 and 1 ton of M2. It has been established that the daily demand for interior paint cannot exceed that for the exterior paint by more than 1 ton. Also, the maximum daily demand for interior paint is 2 tons. The company wants to determine the optimum product mix of interior and exterior paints to maximize the total daily profit given that the profit per ton of the interior paint is 4 thousand dollars and the profit per ton of the exterior paint is 5 thousand dollars.
Please refer to the picture for questions a, b, c, d. Thank you so much.
Find the minimum and maximum values of z=9x+6y, if possible, for the following set of constraints. 3x+6y 2 18 x+6y ≥ 12 x20, y 20 *** Select the correct choice below and, if necessary, fill in the answer box to complete your choice. ⒸA. The minimum value is. (Round to the nearest tenth as needed.) B. There is no minimum value.

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