 4.3.1: Farm Management A farmer has 70 acres of land available for plantin...
 4.3.2: Farm Management A small farm in Illinois has 100 acres of land avai...
 4.3.3: Investment Strategy An investment broker wants to invest up to $20,...
 4.3.4: Investment Strategy A financial consultant wishes to invest up to a...
 4.3.5: Manufacturing Vitamin Pills A pharmaceutical company has 300 kg of ...
 4.3.6: Inventory Blink Appliances has a sale on microwaves and stoves. Eac...
 4.3.7: Banquet Seating A banquet hall offers two types of tables for rent:...
 4.3.8: Spring Break The student activities department of a community colle...
 4.3.9: Nutrition As part of his weightloss routine, Eric plans to only ea...
 4.3.10: Rapid Prototype A computeraided drafting (CAD) instructor at a com...
 4.3.11: Manufacturing A factory manufactures two products, each requiring t...
 4.3.12: Dietary Requirements A diet is to contain at least 400 units of vit...
 4.3.13: Dietary Requirements A certain diet requires at least 60 units of c...
 4.3.14: Production Scheduling In a factory, machine 1 produces 8inch plier...
 4.3.15: Home Mortgages Fremont Bank offered noclosingcost home mortgages ...
 4.3.16: Return on Investment An investment broker is instructed by her clie...
 4.3.17: Maximizing Profit on Ice Skates A factory manufactures two kinds of...
 4.3.18: Maximizing Profit on Figurines A factory manufactures two kinds of ...
 4.3.19: Pollution Control A chemical plant produces two compounds A and B. ...
 4.3.20: Baby Food Servings Gerber Banana Plum Granola costs $0.89 per 5.5o...
 4.3.21: Production Scheduling A company produces two types of steel. Type 1...
 4.3.22: TV Advertising Nielsen TV ratings indicated that during the week of...
 4.3.23: Diet Dannys Chicken Farm is a producer of frying chickens. In order...
 4.3.24: Risk Management The table below shows the price per share at the cl...
 4.3.25: Financial Planning In March 2010, a couple plans to invest $45,000 ...
 4.3.26: Maximizing Rates of Return The table lists two mutual funds: the Jo...
 4.3.27: Maximizing Income J. B. Rug Manufacturers has available 1200 square...
 4.3.28: The rug manufacturer in finds that maximum income occurs when no hi...
 4.3.29: Refer to Example 5. What would you do to eliminate the excess capac...
Solutions for Chapter 4.3: Models Utilizing Linear Programming with Two Variables
Full solutions for Finite Mathematics, Binder Ready Version: An Applied Approach  11th Edition
ISBN: 9780470876398
Solutions for Chapter 4.3: Models Utilizing Linear Programming with Two Variables
Get Full SolutionsThis textbook survival guide was created for the textbook: Finite Mathematics, Binder Ready Version: An Applied Approach, edition: 11. Finite Mathematics, Binder Ready Version: An Applied Approach was written by and is associated to the ISBN: 9780470876398. This expansive textbook survival guide covers the following chapters and their solutions. Since 29 problems in chapter 4.3: Models Utilizing Linear Programming with Two Variables have been answered, more than 16168 students have viewed full stepbystep solutions from this chapter. Chapter 4.3: Models Utilizing Linear Programming with Two Variables includes 29 full stepbystep solutions.

Augmented matrix [A b].
Ax = b is solvable when b is in the column space of A; then [A b] has the same rank as A. Elimination on [A b] keeps equations correct.

Column space C (A) =
space of all combinations of the columns of A.

Determinant IAI = det(A).
Defined by det I = 1, sign reversal for row exchange, and linearity in each row. Then IAI = 0 when A is singular. Also IABI = IAIIBI and

Diagonal matrix D.
dij = 0 if i # j. Blockdiagonal: zero outside square blocks Du.

Distributive Law
A(B + C) = AB + AC. Add then multiply, or mUltiply then add.

Fast Fourier Transform (FFT).
A factorization of the Fourier matrix Fn into e = log2 n matrices Si times a permutation. Each Si needs only nl2 multiplications, so Fnx and Fn1c can be computed with ne/2 multiplications. Revolutionary.

Fourier matrix F.
Entries Fjk = e21Cijk/n give orthogonal columns FT F = nI. Then y = Fe is the (inverse) Discrete Fourier Transform Y j = L cke21Cijk/n.

Fundamental Theorem.
The nullspace N (A) and row space C (AT) are orthogonal complements in Rn(perpendicular from Ax = 0 with dimensions rand n  r). Applied to AT, the column space C(A) is the orthogonal complement of N(AT) in Rm.

Identity matrix I (or In).
Diagonal entries = 1, offdiagonal entries = 0.

Indefinite matrix.
A symmetric matrix with eigenvalues of both signs (+ and  ).

Independent vectors VI, .. " vk.
No combination cl VI + ... + qVk = zero vector unless all ci = O. If the v's are the columns of A, the only solution to Ax = 0 is x = o.

Inverse matrix AI.
Square matrix with AI A = I and AAl = I. No inverse if det A = 0 and rank(A) < n and Ax = 0 for a nonzero vector x. The inverses of AB and AT are B1 AI and (AI)T. Cofactor formula (Al)ij = Cji! detA.

Outer product uv T
= column times row = rank one matrix.

Pascal matrix
Ps = pascal(n) = the symmetric matrix with binomial entries (i1~;2). Ps = PL Pu all contain Pascal's triangle with det = 1 (see Pascal in the index).

Plane (or hyperplane) in Rn.
Vectors x with aT x = O. Plane is perpendicular to a =1= O.

Rank one matrix A = uvT f=. O.
Column and row spaces = lines cu and cv.

Similar matrices A and B.
Every B = MI AM has the same eigenvalues as A.

Symmetric matrix A.
The transpose is AT = A, and aU = a ji. AI is also symmetric.

Tridiagonal matrix T: tij = 0 if Ii  j I > 1.
T 1 has rank 1 above and below diagonal.

Vector addition.
v + w = (VI + WI, ... , Vn + Wn ) = diagonal of parallelogram.