Orthogonality

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 following: • No single surgery will exceed 30% of the total surgeries • No single surgery will be less than 5% of the total surgeries • No single doctor will have more than 45% of the total surgeries • No single doctor will have less than 10% of the total surgeries • The total number of patients must be an integer (set the constraint to "int") Using Linear Pro... click for more

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 station requires 2 hours of machining and welding time and 1 hour of painting and finishing time, and each pec-dec station rquires 2 hours of machining and welding and 2 hours of painting and finishing time. In addition, 2 hours are spent assembling, testing and packaging each body Plus 100. The raw material costs are $450 for each frame, $300 for each press station, and ... click for more

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? c. What is the value of the optimal solution? d. Which constraints are binding? e. Which slack or surplus variables is zero? Please see attached for other Problems.

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 quality level of at least 8 and heating oil, at least 6. Demand for each product is created by advertising. Each dollar spent advertising gasoline creates 5 barrels of demand and each spent on heating oil creates 10 barrels of demand. Gasoline is sold for $25 per barrel, and heating oil for $20. Formulate an LP model to help Saudi Oil maximize its profits. (Assume that nei... click for more