Llinear Programming Models

1. Which of the following mathematical relationships could be found in a linear programming model? And which could not (why)? a. -1A + 2B < 70 b. 2A – 2B = 50 c. 1A – 2B2 < 10 d. 3 squareroot A + 2B > 15 e. 1A + 1B = 6 f. 2A + 5B + 1AB < 25 2. Find the solutions that satisfy the following const ...continues

Quantitative Methods - Linear Program Graphic Solution Procedure

1. For the linear program: Max 2A + 3B s.t. 1A + 2B < 6 5A + 3B < 15 A,B > 0 Find the optimal solution using the graphical solution procedure. What is the value of the objective function at the optimal solution? 2. Solve the following linear program using the graphical solution procedure. Max 5A + 5B s.t. 1A < ...continues

Quantitative Methods : Linear Programming

1. For the linear program: Max 4A + 1B s.t. 10A + 2B < 30 3A + 2B < 12 2A + 2B < 10 A, B > 0 a. write this in standard form. b. solve the problem using the graphic solutions procedure. c. what are the values of the three slack variables at the optimal solutions? 2. Consider the follwoing linear program: Min 2A ...continues

Composite Trapezoidal Rule, Simpson's Rule and Gaussian Quadratures

1. Use the composite Trapezoidal Rule with indicated values of n=4 to approximate the following integrals See Attached file for integrals. 2. Use the Excel programs for Simpson’s composite rule to evaluate integrals in Problem 1. 3. Use Gaussian Quadratures with n = 2, n = 4, n = 5 to evaluate integrals in Problem 1. ...continues

Periodic Functions : Bounded and Continuous

1. A function f:R-->R is said to be periodic if there is a number p > 0 such that f(x) = f(x+p) for all xER . Show that a continuous periodic function on R is bounded and uniformly continuous.

Differentiable Functions and Inverses

1. Let be a differentiable function such that (0) = 0 and for all . a) Show that is strictly monotone and therefore its inverse exists. b) Assume that exists. Compute Please see the attached file for the fully formatted problems.

Taylor Expansion and Remainder

Please see the attached file for the fully formatted problems.

Discontinuous Functions and Riemann Integrability

Let f be a bounded function on [a, b] with finitely many discontinuous points. Prove that f is Riemann integrable.

Mean, Median, Mode and Standard Deviaton

1. Suppose you have administered a test of manual dexterity to two groups of 10 semi-skilled workers. one of these two groups of workers will be employed by you to work in a ware house with many fragile items. the higher the manual dexterity of a worker the less likelyhood that worker wil break significant inventory.Because of a ...continues

Maclaurin Series, Lagrange Interpolation Polynomial and Newton's Interpolation Formulas

1.Expand the following function into Maclaurin Series (see attached file) using properties of the power series. 2. The Lagrange interpolation polynomial may be compactly written as is a shape function. Sketch the shape function in a graphic form. 3. Write a forward and backward difference Newton’s interpolation formulas b ...continues