Consider the following algorithm for solving a linear program in standard form without having to use the Big-M method: Choose any basis. Check to see if this basis is primal feasible. If so, use this as your initial BFS and solve the problem with simplex. If the basis is primal infeasible, solve the problem using dual si
Consider a symmetric square matrix A and the following linear program: Min cx St Ax > c x > 0 Prove that if x* satisfies Ax* = c and x* > 0 then x* is an optimal solution to this linear program.
These questions are a part of a Operations Research class with a section on Reliability Theory. (See attached file for full problem description with proper symbols and equations) --- Question Let N be a non-negative, integer-valued random variable, Show that P{N > 0} >= (E[N])2
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Please see the attached document for the question all properly formatted.
A couple has $40,000 to invest. As their financial consultant, you recommend they invest some money in treasury bills that yield 6%, some money in corporate bonds that yield 8%, and some money in junk bonds that yield 10%. A. Prepare a table showing some of the ways this couple can achieve $3,000 per year in income. B.
9-1 Horrible Harry's Horrible Harry's is a chain of 47 self service gas stations served by a small refinery and mixing plant. Each day's product requirements are met by blending feedstocks on hand at midnight. The volumes vary daily, depending on the previous day's refinery output and on bulk receipts. The entire operatio
Consider the linear program: Min -2x-y St x-y<2 x+y<6 x, y> 0 a) By inspection, argue that this problem cannot have an unbounded optimal solution. b) Convert this problem to simplex standard form, enumerate all the basic solutions, identify which ones are feasible, and compute their objective values. c) What
Exercise 4.25 This exercise shows that if we bring the dual problem into standard form and then apply the primal simplex method, the resulting algorithm is not identical to the dual simplex method. Consider the following standard form problem and its dual. minimize x1 + x2 maximize p
5. Bob Brown's 40th birthday party promised to be the social event of the year in Illinois. To prepare, Bob stocked up on the following liquors. Liquor On Hand (ounces) Bourbon 52 Brandy 38 Vodka 64 Dry Vermouth 24 Sweet Vermouth 36 Bob decided to mix four drinks for the party: Chaunceys, Sweet Italians, Bourbon on th
Exercise 4.26 Let A be a given matrix. Show that exactly one of the following alternatives must hold. (a) There exists some x does not equal 0 such that Ax = 0, x > 0. (b) There exists some p such that p'A> 0'. Exercise 4.27 Let A be a given matrix. Show that the following two statements are equivalent. (a) Every vector such
(See attached file for full problem description)
A brewery manufactures 3 types of beer : lite, regular and dark. Each vat of lite beer requires 6 bags of barley, 1 bag of sugar, and 1 bag of hops. Each vat of regular beer requires 4 bags of barley, 3 bags of sugar, and 1 bag of hops. Each vat of dark beer requires 2 bags of barley, 2 bags of sugar, and 4 bags of hops. Each
This question is from linear programming. I want to use duality (it's so obvious), farkas lemma (alternative solution) and all. (See attached file for full problem description with equations) --- (a) Let . Prove that one of the following systems has a solution but not both: (b) Prove or disprove the following cla
1. AA Auto manufactures luxury cars and trucks. The company believes that its most likely customers are high-income women and men. To reach these groups, AA Auto has embarked on an ambitious TV advertising campaign and has decided to purchase 1-minute commercial spots on two types of programs: comedy shows and football games.
See attached file for full problem descriptions with complete equations. --- 1. During the next three months, Ironco faces the following demands for steel: 100 tons (month 1); 200 tons (month 2); 5 tons (month 3). During any month, a worker can produce up to 5 tons of steel. Each worker is paid $5000 per month. Workers c
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
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
Consider the following LP problem min s.t. (a) Suppose we have a very fast routine to solve the problems of the form min s.t. for arbitrary vectors . How would you decompose the problem above the take advantage of such fast subroutine? (b) Suppose we have a very fast routine to solve pr
(See attached file for full problem description) --- Reliable Investment Corporation is in the process of determining its investment strategy for the next three years. Currently (time t = 0), $100,000,000 is available for investment. The cash flow associated with investing $1 in each of the available investment alternatives
I am working to define constraints and am having problems in doing so. I would like a detalied explanation of how this is done and how Lindo will interrprut the information. (See attached file for full problem description) --- A company needs to lease warehouse storage space for five months at the start of the year. Th
The following table is a list of all of the stocks that you have in your stock portfolio. The original purchase price, current price and your best guess for the "anticipated" price (one year into the future) is given below: Share Price ($) Stock # Shares Owned Purchase Current Expected In One Year 1 234 20 30 36 2 272 2
A company needs to lease warehouse storage space for five months at the start of the year. The space requirements (in square feet) and the leasing costs of each type of lease are given in the two tables below: Month Required Space (sq. feet) Jan 15,000 Feb 10,000 Mar 20,000 Apr 5,000 May 25,000 Lease Term (months) Co
Sunco Oil Co. manufactures three types of gasoline: Gas 1, Gas 2 and Gas 3. Each type is produced by blending three type of crude oil: Crude 1, Crude 2 and Crude 3. The sales price per barrel of gasoline and the purchase price per barrel of crude oil is given in the following table: Gasoline Type Gas Selling Price Per Barrel C
In this problem I am trying to get rid of the artificial variable using the two phase method. However all of the rows either have negatives or zeros and my final answer keeps coming out to be a negative and none of the other answers plug into the constraints. The problem is Using Simplex method minimize C:
A biologist must make a nutrient for her algae. The nutrient must contain three basic elements D, E, F, and must contain at least 10kg of D, 12kg of E, and 20Kg of F. The nutrient is made from three ingredients, I, II, III. The quantity of D, E, F in one unit of each of the ingredients is given in the following chart.
Question #1 A company produces three products. The per-unit profit, labor usage, and pollution produced per unit are given in the table 1. At most, 3 million labor hours can be used to produce the three products, and government regulations require that the company produce at most 2 lb of pollution. If we let Xi = units produ
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.
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. ---
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