Linear Programming Models : Graphical Methods

MSA Computer Corporation manufactures two models of minicomputers, the Alpha 4 and Beta 5. The firm employs five technicians, working 60 hours each per month, on its assemble line. Management insists that full employment (i.e. all 160 hours of time) be maintained for each worker during next month's operations. It requires 20 lab ...continues

Linear Programming Models : Risk-Analysis

The winner of the Texas Lotto has decided to invest $50,000 per year in the stock market. Under consideration are stocks for a petrochemical firm and a public utility. Although a long-range goal is to get the highest possible return, some consideration is given to the risk involved with the stocks. A risk index on a scale of 1-1 ...continues

Linear Programming Models : Graphical methods

The dean of the Western College of Business must plan the school's course offering for the Fall semester. Students' demands make it necessary to offer at least 30 undergraduate and 20 graduate courses in the term. Faculty contracts also dictate that at least 60 courses be offered in total. Each undergraduate course taught costs ...continues

Linear Programming : Maximizing Profit

The Outdoor Furniture Corporation manufactures two products, benches and picnic tables, for use in yards and parks. The firm has two main resources: its carpenters (labor force) and a supply of redwood for use in the furniture. During the next production cycle, 1,200 hours of labor are available under a union agreement. The firm ...continues

Comparing Hyperbola Graphs; Practical Uses of Probability

One of the civil engineers you interviewed for your article works for a company which specializes in bridge construction projects. In the process of designing suspension bridges, they must account for many variables in the modeling. Some of these variables include the bridge span; the force of the typical water currents wearing ...continues

Ideals : Cyclic Module in a Commutative Ring

Prove that every cyclic module in a commutative ring R is of the form R/L for some ideal L. //Note: R/L is said "R modulo L"

Linear Algebra: Map on Space of all 5x5 Symmetric Matrices

Let L(A) = A + A^t be a map on the space of all 5x5 symmetric matrices. Prove that L is a linear operator and find its matrix in some basis.

Linear Algebra: 7x7 Matrix, Adjoint and Conjugacy

Let A be a 7x7 matrix. Find all solutions of the equation A^7 = 0 up to conjugacy.

Modules, Polynomial Rings, Finite Dimensional Vector Space and Multiplication

Prove that a module over a polynomial ring C[t] is a finite dimensional vector space with a linear operator that plays the role of multiplication by t.

Give an example of a ring which is not a principle ideal domain.

Give an example of a ring which is not a principle ideal domain.