FarmFresh Foods manufactures a snack mix called TrailTime by blending three ingredients: a dried fruit mixture, a nut mixture, and a cereal mixture. Information about the three ingredients (per ounce) is shown below. Ingredient Cost Volume FatGrams Calories Dried Fruit .35 .25 cup 0 ...continues
Proof of Vertex, Extreme Point, Basic Feasible Solution
Can you please let me know how to approach those proof questions. Consider the polyhedron P = {x Rn : xi > 0 for all i = 1 … n}. a)Prove that the origin (i.e. the vector of all 0's) is a vertex of P, according to the definition of a vertex (i.e. do not rely on the fact that vertex = extreme point = basic feasible ...continues
Justify Linear Programming Statements : Equality Constraints, Vectors and Cross Product
For each statement, state whether it is true or false. Be sure to justify your answer. a) Suppose you are given a linear program in Rn with mE equality constraints and mI inequality constraints. Let x be an element of the polyhedron at which n - mE inequality constraints are active. Then x must be an extreme point of the poly ...continues
Linear Programming : Feasible Solution - Optimal Objective Value of Zero?
Consider a feasible solution y to the linear program Min cx St Ax = b x > 0 Let Z = {i | yi = 0}. Show that y is an optimal solution if and only if the following linear program has an optimal objective value of zero: Min cd St Ad = 0 di > 0 for all i in Z Please see the attached file for the fully ...continues
Simplex Method and Linear Programming : Optimal Basis
a) Consider the following linear program: Min 5a + 4b - c + 2e St a - 2c + d + 2e = 1 3b + 3c + 6d - 9e = 3 a, b, c, d, e > 0 Using the optimality criteria from the simplex method, argue whether or not {a, b} is an optimal basis. ---
Linear Programming: Largest possible adjacent basic feasible solutions
For a given basic feasible solution in a problem in standard form with no degenerate extreme points, what is the largest possible number of adjacent basic feasible solutions that it can have, as a function of n and m? Give an example of when it will be strictly fewer than this number.
(See attached file for full problem description)
Feasibility of a Linear Programming Problem
Exercise 3.22 Consider the following linear programming problem with a single constraint: minimize Σ i=1 --> n cixi subject to = ... i=1,...,n. (a) Derive a simple test for checking the feasibility of this problem. (b) Assuming that the optimal cost is finite, develop a simple method for obtaining an optimal soluti ...continues
Linear Programming : Adjacency of Basic Feasible Solution and Hyperplanes
Can anyone finish up this proof by continuing my preliminery work? I started but can't finish this. I know starting by adding up the point z is correct way, but just can't continue to show if and only if. (See attached file for full problem description) --- Assume , , with rank (A) = m are given. Two different basic ...continues
Condition when dual is identical to the primal
(See attached file for full problem description)
