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
A customer requires during the next four months, respectively, 50, 65, 100, and 70 units of a commodity (no backlogging is allowed). Production costs are $5, $8, $4, and $7 per unit during these months. The storage cost from one month to the next is $2 per unit (assessed on ending inventory). It is estimated that each unit o
My Oil Company has 5,000 barrels 1 of oil and 10,000 barrels of oil 2. The company sells two products: gasoline and heating oil. Both products are produced by combining oil 1 and oil 2. The quality level of each oil is as follows: oil 1 -- 10; oil 2 -- 5. Gasoline must have and average quality level of at least 8, and heati
I have to determine how much investment and debt to undertake during the next year. Each dollar invested reduces the NPV of my company by 10 cents, and each dollar of debt increases the NPV by 50 cents (due to deductibility of interest payments). I can invest at most $1 million during the coming year. Debt can be at most 40%
Each day workers at Sprinfield Mall parking lot work two 6 hour shifts from 12 A.M. to 6 A.M., 6 A.M. to 12 P.M., 12 P.M. to 6 P.M., and 6 P.M. to 12 A.M. The following number of workers are needed during each shift: 12 A.M. to 6 A.M. - 15 workers; 6 A.M. to 12 P.M. - 5 workers; 12 P.M. to 6 P.M. - 12 workers; 6 P.M. to 12
Can anyone help me to prove this? I'm really stuck with geometry in Linear Programming... (See attached file for full problem description and equations) --- Assume P is a polyhedron and H is a supporting hyperplane to P. Prove that is an extreme point of if and only if is an extreme point of P.
Find the complete optimal solution to this linear programming problem. Min 3X + 3Y s.t. 12X + 4Y > 48 10X + 5Y > 50 4X + 8Y > 32 X , Y > 0
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
Question 1 Cully furniture buys 2 products for resale: big shelves (B) and medium shelves (M). Each big shelf costs $500 and requires 100 cubic feet of storage space, and each medium shelf costs $300 and requires 90 cubic feet of storage space. The company has $75000 to invest in shelves this week, and the warehouse has 1800
Why should decision makers who are primarily concerned with marketing or finance or production know about linear programming?
(See attached file for full problem description) --- Indicate whether the sentence or statement is true or false. _____ 1. Determining the production quantities of different products manufactured by a company based on resource constraints is a product mix linear programming problem. _____ 2. When using linear program
(See attached file for full problem description) --- Consider the following linear programming problem... --- (See attached file for full problem description)
Explain a process more clearly. --- - Minimize... - Duality Principle... - Transposing Matrices... - Pivot Operation --- Please see the attached file for the fully formatted problems.
Can you show me step by step how to create and solve linear problems using Excel?
(See attached file for full problem description) 1.) Without graphing, determine which of the following three points: P1 = (8,6) P2 = (2,5) P3 = (4,1) are part of the graph of the following system: y - 10x <= 0 2y - 3x >= 0 y + x <= 15 ________________________________________ 2.) Maximiz
(See attached file for full problem description) --- 1) Discuss from your own experience a case where you had to maximize or minimize something and also how you think linear programming techniques might have helped you arrive at your final decision. 2) Read the short, well-written article on the Simplex Method which
Homework problems. File is attached. --- True/False Indicate whether the sentence or statement is true or false. ______ 1. A linear programming model consists of decision variables, constraints, but no objective function. ______ 2. Linear programming models exhibit linearity among all constraint relationships and th
Linear Programming Models in Excel (Solver) TABLE: Hours for Judicial 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 and can handle up to 120 hours per month of casework. To avoid a backlog, all c
The problem is from Numerical Methods. Please show each step of your solution and tell me the theorems, definitions, etc. if you use any. If there is anything unclear in the question, let me know. Thank you. Write a program that takes the output A and p from (a), along with a right hand side b, and computes the solution....
See attch for problem Consider the following linear programming problem: Maximize 3x -y subject to: 6x - 5y, < 24 x + 9y > 63 x > 0, y > 0 Which of the following is the initial simplex tableau? A) x y u v M 6 -5 1 0 0 24 1 9 0 1 0 63 -3 1
Consider the simplex tableau: x y z u v M 2 1 0 -3 8 0 2 3 0 1 5 2 0 5 1 0 0 6 5 1 19 The tableau is the final one in a problem to maximize x+2y+3z. The maximum value of x+2y+3z occurs when: a. x = 2, y=5, z=0 b. x=2
The result of pivoting the simplex tableau x y u v M -2 1 1 0 0 0 6 4 0 -1 0 42 1 -2 0 0 1 0 About -2 (1st row, 1st column) is: a) x y u v M 1 -1/2 -1/2 0 0 0 0 7 3 1 0 84 0 -3/2 ½ 0 1
See Attached for problem Consider the following linear programming problem: Maximize 10x + 7y subject to: x + 3y < 10 2x -y < 8 x > 0, y > 0 The initial simplex tableau is: A) x y u v M 1 3 1 0 0 10 2 -1 0 1 0 8 -2 -1 0 0 1 0 B)
The particular solution corresponding to the simplex tableau x y u v M 0 -3 1 1 0 2 1 2 0 0 0 6 0 -4 0 5 1 10 is: a. X=2, y=6, u=10, v=0, M=0 b. X=2, y=6, u=0, v=0, M=0 c. X=6, y=0, u=0, v=0, M=10 d. X=6, y=o, u=6, v=0, M=10 e. None of the above
See attach for problem. The linear programming problem. Minimize 5x - y subject to: -2x - 2y < 12 -3x + 2y > 0 x > 0, y > 0 is equivalent to the linear programming problem: a. Maximize 5x - y subject to: -2x -2y < 12 3x - 2y < 0 x > 0, y > 0 b. Maximize 5x-y subject to: -2x -2y
Consider the feasible set attached. The maximum value of the objective function 6x = 3y is a. 24 b. 20 c. 12 d. -6 e. none of the above
See attachment for problem.
New cars are transported from docks in Baltimore and New York to dealerships in Pittsburgh and Philadelphia. The dealership in Pittsburgh needs 20 cars and the delaership in Philadelphia needs 15 cars. It costs $60 to transport a car from Baltimore to Pittsburgh, $45 to transport a car from Baltimore to Philadelphia, $65 to tr
In the following simplex tableau, the next pivot element is (see attachment): x y u v M 2 1 0 5 0 20 4 0 1 8 0 32 -3 0 0 2 1 -9 a. 4 in the second row, first column b. 8 in the second row, fourth column c. 1 in the first row, second column d. -3 in the third row
Consider the simplex tableau x y u v w M 1 0 3 0 0 0 10 0 0 1 0 1 0 0 0 1 -6 0 0 0 3 0 0 8 1 0 0 7 0 0 5 0 0 1 4 The tableau above is the final one in a problem to minimize -x + 2y. The minimum value of -x + 2y