Use the simplex method to maximize the following (you must show your work) : Maximize f = 5x1 + 7x2 + 8x3 subject to x1 + 4x2 + 5x3 < 30 3x1 + 2x2 + 4x3 < 16 x1 + 5x2 + 2x3 < 14 x1 2 0, x2 2 0, x3 > 0
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- Maximize p = 7x + 6y + 3z subject to x + y + z ≤ 150 x + y + z ≥ 100 x ≥ 0, y ≥ 0, z ≥ 0. p= (x, y, z)=Consider the Max LP: min w I1, I2 Decide if this is a normal max LP (but I decided not to ask) (y₁ ≥ 0) Y₁ (Y/2 ≥ 0) Y2 (Y3 > 0) Y3 x = 3x1 + 201 8.t. 21 +2 X1 + X2 I1 2. Here is a the table form for finding the dual, but there is a couple of missing or incorrect entries that you are asked to identify below it: the value of a is cis max z (*₁ ≥ 0) (*₂ > 0) Ta 1 1 21 2 1 100 ≤80 ≤40 >0 a 2 the missing value(s) in position b is (are) no extra spaces though) 3. The objective function for the dual min is w = cy1 + dy2 + e y3 where and d is <100 <80 <40 and e is (as we usually write thingsPlease do not give solution in image formate thanku. 11-24 Using PERT, Ed Rose was able to determine that the expected project completion time for the construction of a pleasure yacht is 21 months and the project variance is 4. What is the probability that the project will be completed in 17 months or less? What is the probability that the project will be completed in 20 months or less? What is the probability that the project will be completed in 23 months or less? What is the probability that the project will be completed in 25 months or less?
- A simplex tableau is shown below. You should complete the tableau and respond to the questions posed. Basis CB cj JIN Cj Zj X1 3 1 X2 4 x3 0 0 5 1/2 0 1 S1 O 1/2 S2 O -1/2 6 -1/4 1 What is the current value of the objective function of the current simplex tableau? (round to 2 decimal places) 3For a certain civil engineering system, it is sought to maximize the benefits, which is given by the expression: Z=3x+5y. The decision variables are x (the amount of resource type 1 to be used) and y (the amount of resource type 2 to be used). • The amount of resource type 1 should be at least 3 units. • The amount of resource type 2 should be at least 3 units. The difference between the amount of ● resource type 2 and the amount resource type 1 should not exceed 6. • The total amount of resource types 1 and 2 should not exceed 12 units. a. Identify the obiective function for this problem. b. Identify and write the constraints. c. Provide a sketch graph for the constraint set. d. Clearly show the feasible region. e. Label all extreme points (or vertices) of the feasible region and indicate their coordinates. f. Solve the optimization problem.A survey was conducted to 12 first time voters on their preferred candidate. The results are: BBM, BBM, LR, IM, PL, PL, IM, IM, BBM, BBM, LR, LR. Which statement is true? The Borda score of PL is two points. BBM wins by plurality method. The Condorcet winner is IM. The modes are LR and IM Which of the following is a property of all linear programming problems? alternate courses of action to choose from minimization of some objectives a computer program usage of graphs in the solution
- 4 For each of the following, determine the direction in which the objective function increases: a z = 4x, - x2 b z = -x, + 2x2 C z = -x - 3x2minimize Z = 5x1 + x2 subject to 3x1 + 4x2 = 24 0 x1 x1 + 3x2A firm is currently taking on two projects with an individual cost of capital of 10 percent and 12 percent for each of the projects. That means that the before tax cost of capital for the firm must be between 10 and 12 percent Select one: a. False b. True
- . A group of students organizes a bake sale in which they sell hundreds of cookies at $1per piece. They set up a table on campus and wait for students to come and purchasetheir cookies. Consider the following variables in this bake sale operation:1. Size of the cookies2. Weather conditions on campus3. Organization of the table4. Number of cookies sold5. Competition from other fund-raisers coinciding on campus6. Amount of advertising and shouting of the students at the bake sale table7. Number of students on campus that dayWhich of these variables is an output variable?a. 3b. 4c. 5d. None of the abovemax 100x1+160x2 st 8x1 + 6x2 <= 480 4x1 + 2x2 <= 360 6x1 + 18x2 <= 7209.5 Capital Healthplans Inc. is evaluating two different methods for providing home health services to its members. Both methods involve contracting out for services, and the health outcomes and revenues are not affected by the method chosen. Therefore, the net cash flows for the decision are all outflows. Here are the projected flows: Year Method A ($) Method B ($) 0 (300,000) (120,000) 1 (66,000) (96,000) 2 (66,000) (96,000) 3 (66,000) (96,000) 4 (66,000) (96,000) 5 (66,000) (96,000) What is each alternative’s IRR? If the opportunity cost of capital for both methods is 9 percent, which method should be chosen? Why?