1. Show that ||x||∞ = max |xi|, 1 ≤ i ≤ n defines a norm on R^n. 2. Let Q be an n x n orthogonal matrix. Use mathematical induction to prove each of the following. A) (Q^m)^-1 = (Q^T)^m = (Q^m)^T for any positive integer m. B) ||Q^m*x|| = ||x|| for any x Є R^n.
Linear Programming Using Excel
You are managing the OR and have been told to come up with the mix of surgeries and doctors that will yield $2,300,000. Currently your OR performs 5 different surgeries and has 3 different doctors. Your OR operates one shift per day with a maximum amount of 8,000 OR hours. The only constraints that you have been given are the fo ...continues
Modeling Problem: Two Decision Variables (Linear Programming/Optimal Solution)
A manufacturer of excercise equipment will begin production of two types of machines: Body Plus 100 and Body Plus 200. The Body Plus 100 consists of a frame unit, a press station, and a pec-dec station. each frame produced uses 4 hours of maching and welding time and 2 hours of finishing and painting time. Each press statio ...continues
Objective Function, Constraints, Optimal Solutions - Linear Equations
PROBLEM 1 1. Use this graph to answer the questions. Maximize 28X + 35Y Subject to: 12X + 15Y < 180 15X + 10Y ≥ 150 3X - 8Y < 0 X , Y > 0 a. What is the feasible region (I, II, III, IV, or V)? b. Which point (A, B, C, D, or E) is optimal? ...continues
Decision Variables, Contraints & Objective Function
Homework Problem Saudi Oil Company has 5000 barrels of Type A oil and 10000 barrels of Type B oil. The company sells two products: Gasoline and Heating Oil. Both products are produced by combining Type A and Type B oil. The "quality level" of Type A oil is 10 and that of Type B oil is 5. Gasoline must have an average quali ...continues
linear programming and game theory - 2 problems
Consider the linear programming problem: Max 6x1 + 14x2 + 13x3 subject to: ½x1 + 2x2 + x3 ≤24 x1 + 2x2 + 4x3 ≤ 60 x1, x2, x3 ≥ 0. along with the optimal dictionary x1 = 36 - 6x2 - 4s1 + s2 x3 = 6 + x2 + s1 - ½s2 _________________________ z = 294- 9x2 -11s1-½s2 ( ...continues
Suppose you have N jobs that have to be processed on a single machine. For i = 1, 2, . . . ,N, job i requires pi units of time on the machine, and has weight wi. The objective is to schedule these jobs so as to minimize the sum of the weighted completion time of all the jobs, where the completion time of job i is the time at w ...continues
Linear Programming using Excel
Linear Programming Models in Excel (Solver) -------------------------------------------------------------------------------- TABLE: Hours for Judical Problem Jan 400 July 200 Feb 300 Aug 400 Mar 200 Sept 300 April 600 Oct 200 May 800 Nov 100 June 300 Dec 300 Suppose each judge works all 12 months a ...continues
Please help me to find out how I can do this (See attached file for full problem description) --- Let (see attachment) It is clear that we can rewrite (attached) as (attached) , i.e. as a system of linear inequalities. (I've done this). Show that in fact we can rewrite (attached) as a system of (attached) linear i ...continues
Proof of Dual using Farkas Lemma (PhD)
Hello, Could you please help me to prove this using Farkas Lemma? Well, I initially thought that I can use Farkas Lemma, but if it is impossible to use the lemma (though I do belive it will help), you might try other way. Thank you! --- (See attached file for full problem description)
