Please solve everything write the simplex tableau for the given linear pro-gramming problem. You do not need to solve the problem. (In eachcase the objective function is to be maximized.)1. Objective function:z = x1 + 2x,2. Objective function:z = x1 + 3x,Constraints:Constraints:X1 + x,54X1 - X,<12x1 + x2< 8X1 + x,55X1, X,2 0X1, X, 2 03. Objective function:z = 2x1 + 3x, + 4x34. Objective function:z = 6x1 – 9x,Constraints:Constraints:X1 + 2x2< 122x, - 3x, < 6X1 + x2< 20X1, X, 2 0X1+ x3< 8X1, X2, X32 0 use the simplex method to solve the givenlinear programming problem. (In each case the objective functionis to be maximized.)9. Objective function:z = x1 + 2x,10. Objective function:z = x1 + x2Constraints:Constraints:X1 + 4x, s 8X1 + x2< 12X1 + 2x, s 63x, + 2x, < 12X1, X22 0X1, X2 2 0

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Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter7: Nonlinear Optimization Models

Section: Chapter Questions

Problem 49P: If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60...

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If a monopolist produces q units, she can charge 400 4q dollars per unit. The variable cost is 60 per unit. a. How can the monopolist maximize her profit? b. If the monopolist must pay a sales tax of 5% of the selling price per unit, will she increase or decrease production (relative to the situation with no sales tax)? c. Continuing part b, use SolverTable to see how a change in the sales tax affects the optimal solution. Let the sales tax vary from 0% to 8% in increments of 0.5%.
1. If constraint has a shadow price of $6, Right-Hand-Side (RHS) is 12, allowable increase is 2, allowable decrease is 4. How would objective function change if the RHS of this constrains changes from 12 to 9? Answer___________
To formulate a minimization problem for solution by the simplex method, we must add slack variables to a. only inequality constraints. b. only “less than” constraints. c. only “greater than” constraints. d. all inequality constraints.
1. A specific assignment of values to decision variables is called what? a. Constraint b. Feasible c. Solution d. None of the above 2. Which of the following must be true of a feasible solution a. All of what Solver calls changing variables must be greater than 0 b. It is optimal c. It violates no constraints d. None of the above
In preparing a ≥ constraint for an initial simplex tableau, you would a. add a surplus variable. b. add slack variable. c. subtract an artificial variable. d. subtract a surplus variable and add an artificial variable.
Consider the following set of constraints (Maixmization problem): 43X+ 86Y>= 29, and 129X+ 43Y >= 14.5. The following is true for this problem: a. Unbounded problem. b. X = 0, Y = 43 is the only optimal solution. c. X=43, Y=-7 is the only optimal solution. d. Infeasible problem. Clear my choice
Formulate a linear program for this problem. 2) A hydroelectric dam needs to schedule how much power to produce in each of the next 24 hours. The demand in megawatts (MW) in hour t = 1, ..., 24 is dị. The power plant must produce at least the demand for each hour, but can produce more at a cost of K dollars per excess MW. For engineering reasons (can't open/close waterways too fast), after hour 1 the production in any given hour must be within 10 MW of the previous hour's production. For example, producing 25 MW in hour 3 means in hour 4 we have to produce between 15 and 35 MW. Finally, the combined production over 24 hours cannot exceed the reservoir capacity R. Please note that d, K, R are parameters, i.e. known values.
Solve the following Linear Programming model using the graphical method (USING EXCEL){Write the steps of construction} Q1)MaximizeH = x + 3y Objective functionsubject tox + y ≤ 502x + y ≤ 60 x ≥ 0, y ≥ 0
Consider the following set of constraints: 48Y >= 7296; 0.25 X + 12Y >= 1824, and X + Y <= 152. Pick a suitable statement for this problem: a. Solution to this problem cannot be found without the objective function. b. The feasible region is defined by a single (unique) point. c. It is a non-linear problem - unsuitable for grphical method. d. This problem has two feasible points - one is optimal for miniization problem and other is optimal for maximization problem. e. Feasible region is represented by a line and multiple feasible points are available.
Use simplex method for linear programming. Show solution for each iteration table. Problem: A small firm that assembles computers is about to start production of two new types of personal computers. Each type will require assembly time, inspection time, and storage space. The amount of each of these resources that can be devoted to the production of the computers is limited. The manager of the firm would like to determine the quantity of each computer to produce in order to maximize the profit generated by sales of these computers. In order to develop a suitable model of the problem, the manager has met with design and manufacturing personnel. As a result of those meetings, the manager has obtained the following information: Type 1 Type 2 Profit per unit $60 $50 Assembly time per unit 4 hours 10 hours Inspection time per…
9. Which of the following is NOT a requirement of a linear programming problem? Select one: a. constraints, expressed as linear equations or inequalities b. an objective function to be maximized or minimized c. an objective function, expressed in linear terms d. alternative courses of action e. one constraint for each decision variable
For the products A, B, C, and D, which of the following could be a linear programming objective function? Select one: a. Z = 1A + 2BC + 3D b. Z = 1A + 2AB + 3ABC + 4ABCD c. Z = 1A + 2B + 3C + 4D d. Z = 1A + 2B/C + 3D

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