prove it .The set of all optimum solution of the general convex programming problem is a convex
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prove it .The set of all optimum solution of the general convex programming problem is a convex set
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- The situation in which the value of the solution may be made infinitely large in a maximization linear programming problem or infinitely small in a minimization problem without violating any of the constraints is known as. The __________ assumption necessary for a linear programming model to be appropriate means that the contribution to the objective function and the amount of resources used in each constraint are in accordance to the value of each decision variable. In problem formulation, the a. nonnegativity constraints are always ignored. b. optimal solution is decided upon. c. objective is expressed in terms of the decision variables. d. constraints are expressed in terms of the obtained objective function coefficients. Which of the following error messages is displayed in Excel Solver when attempting to solve an unbounded problem?The dual of a linear programming problem have a finite optimal solution, then the primal possess a no solution finite optimal solution unbounded solution infinite solutiona) Specify whether the following axioms are true or false. An LP problem is an optimization problem for which we do the following: i. We attempt to optimize a linear function of the decision variables. ii. Each constraint must be a linear equation or linear inequality. i. The values of the decision variables must satisfy some sets of constraints.
- 1. Set up a linear programming model of the situation described. Determine whether it is in standard form. If not make it standard. A restaurant chef is planning a meal consisting of two foods, A, and B. • Each kg of A contains 3 units of fat and 6 units of protein • Each kg of B contains 1 unit of fat and 3 units of protein The chef wants the meal to consist of at least 18 units of protein and at most 6 units of fat. If the profit that he makes is 3 dollars per kg for food A and 5 dollars for food B, how many kilograms of each food should be served so as to maximize his profit?Solve the linear programming problem. (If there is no solution, enter NO SOLUTION.) Maximize z = 3x − 7y Subject to y ≤ x y ≤ 70 y ≥ 35 x ≤ 95 The maximum value of z is __ at(x, y) = ( __ , __ ).List the corner points for the following collection of constraints of a linear programming problem. x ≤ 13 4x + 6y224 X20 y20 a. (0,4), (6, 0), (13,0) b. (0, 0), (6, 0), (0, 13) c. (0, 0), (0, 4), (13,0) d. (0,4), (0, 24), (13, 0) e. (0, 0), (6, 0), (13,0) O O
- e. Write out the standard form a standard convex optimization problem and show that the feasible set and the solution set of a standard convex optimization problem are convex.Choose Yes or No to indicate whether each of the following statements about the CONVEXITY OR CONCAVITY of an OBJECTIVE FUNCTION of convex programming problems is true. Objective function may exist and may be concave Objective function may exist and may be convex Objective function may exist and may be neither convex nor concave Objective function may exist and must be concave Objective function may exist and must be convex Objective function may exist and must be neither convex nor concave Objective function must exist and must be concave Objective function must exist and must be convex Objective function must exist and must be neither convex nor…The owner of the Consolidated Machine Shop has $10,000 available to purchase a lathe, a press, a grinder, or some combination thereof. The following 0–1 integer linear programming model has been developed to determine which of the three machines (lathe, x1, press, x2, or grinder, x3) should be purchased in order to maximize annual profit: Maximize Z = 1000x1 + 700x2 + 800x3 (profit, $) subject to: $5,000x1 + 6,000x2 + 4,000x3 ≤ 10,000 (cost, $) x1 , x2 , x3 = 0 or 1 1. Solve this model by using the computer.
- Using the graphical algebralc method, the optimal solution to a linear programming problem, if exists, it occurs at O a point in the x-axis O a corner of the feasible region. o the point (0,0) o a point in the y-axisIn a goal programming problem with two goals at the same priority level, all the deviational variables are equal to zero in the optimal solution. This means: there is no feasible solution to the problem all goals are fully achieved this problem was an integer programming problem None of the provided options nonlinear programming must be used to solve thisHelp!