Linear Programming - Investment and Debt : Maximizing Net Present Value ( NPV )

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% ...continues

Linear Programming : Maximizing Profit

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 ...continues

Linear Programming : Maximizing Revenue

A company produces A, B, and C and can sell these products in an unlimited quantities at the following prices: A - $10; B - 56; C - $100. Producing a unit of A requires 1 hour of labor; a unit of B, 2 hours of labor plus 2 units of A; and a unit of C, 3 hours of labor plus 1 unit of B. Any A that is used to produce B cannot be ...continues

Linear Programming : Minimizing Net Cost

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 ...continues

Linear Programming : Scaling, Unbounded LPs and Feasible Region

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 ...continues

A company needs to lease warehouse storage space

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 ...continues

Linear Programming : Using Lindo or Excel to Develop Constraint Equations

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 ...continues

Vectors and Matrices : Matrix Operations on Row Vectors

1. Take the following three row vectors: A = (1, 3), B = (7, 9), C = (7, 2) 1. Find the column vectors V = AT, W = BT, X = CT 2. Create the Matrix D such that A is the first row, B is the second row, and C is the third row 3. Create the Matrix E such that V is the first column, W is the second column, X is the third column 4 ...continues

Vector and Matrix Operations : Row Vectors, Column Vectors, Dot Product and Echelon Form

1. Find the dot product for the following pairs of vectors: a. Row vector = (2 0) Column vector is below 5 18 b. Row vector = (3 9 -4) Column vector is below 3 0 2 c. Row vector = (5 6 7 8) 1 1 1 1 The following matrices will be used in problems 2-3 below: 0 -2 5 A= 3 -4 17 1 2 3 9 7 2 -3 ...continues

Systems of Linear Equations : Row Operations and Solutions

1. Find the augmented matrix for each system of linear equations: a. 5x1 + 7x2 + 8x3 = 3 -2x1 + 4x2 + 9x3 = 3 3x1 - 6x2 + x3 = 1 b. 4x1 + x2 - 7x3 = 6 5x1 + 7x2 + 2x3 = 3 5x1 + 2x2 + 5x3 = 7 c. 3x1 - 2x2 + 2x3 = 7 5x1 + 7x2 + 3x3 = 3 -5x1 + 6x2 - 8x3 = -5 2. Using elementary row operations reduce each of the augm ...continues