#### Decision Tree using Palisade Precision Tree

The senior executives of an oil company are trying to decide whether or not to drill for oil in a particular field in the Gulf of Mexico. It costs the company \$300,000 to drill in the selected field. Company executives believe that if oil is found in this field its estimated value will be \$1,800,000...

#### Space Constrained Inventories

A grocer has exactly 1,000 square feet available to display and sells 3 kinds of vegetables. The space consumed by each kind of vegetable is proportional to its cost, and tomatoes consume 0.5 square feet per pound. There is a \$100 setup cost for replenishing any of the vegetables, and the interest...

#### Linear programming for Burger Doodle

This must all be done in Excel. (Very Important) I have also put a link of an example problem for the first part. This how I would like it formatted. Please take a look at it for reference. http://documents.saintleo.edu/docs/AVP/MBA550/MBA550_ch9.mp4 The manager of a Burger Doodle franchise ...

#### Linear Programming Using a Demand Function

I am trying to use Linear Programming to solve the attached equation. Accordingly, I used a Demand Function and determined the variable coefficients. I have been receiving comments stating that the problem is unclear and ambiguous. Thus, I tried cleaning it up a bit. The idea is to show the meth...

#### Real Life Scenarios: Systems of Linear Equations

Determine a simple real-life example scenario to solve systems of linear equations - Discuss how the math concept applies to your scenario. Scenarios or examples should clearly demonstrate how the math principle can be used to solve a real-life problem. - Research and include references format...

#### Find the range of optimality for Cx

You are given a linear programming problem that has already been solved. The following conditions hold: (i) You are maximizing the objective function 6x + 5y (ii) After solving the problem, you found that the optimal solution point occurs at the intersection of exactly two of the constraints, nam...

#### Formulate the following network problem

(See the attached file for the diagram) - In the above network, a given flow Q is transferred through the network to a demand node N. The goal is to route the flows in such a way that total channel loss is minimized, where channel loss coefficients clij per unit length are given for each link or...

#### Analytical Models in DSS

A company that assembles electronic alarm systems requires three component parts: C1, C2, and C3. In-house production costs are estimated to be \$15 per unit for part C1, \$18 per unit for part C2, and \$ 20 per unit for part C3. It requires 0.16 hours of machining time and 0.1 hours of finishing time...

#### Sensitivity Analysis and LP Solve

Transportaton Problem (Minimal Cost) There are three warehouses at different cities: Tauranga, Wanganui and Wellington. They have 180, 100 and 150 tons of paper available over the next week respectively. There are four publishers in Auckland, Palmerston North, Hamilton and Wellington. They have o...

#### Linear Mapping in Subsets

Question 1. 1) Suppose (V, | * |) is a normed space. If x, y E V and r is a positive real number, show that the open r-balls Br(x) and Br(x + y) in V are homeomorphic. 2) Suppose V and W are two normed spaces. If A : V ---> W is a linear map, then show that it is continuous at every point v E V ...

#### Network Flow using Nodes and Links

A manufacturer must produce a certain product in sufficient quantity to meet contracted sales in the next four months. The production facilities available for this product are limited, but by different amounts in the respective months. The unit cost of production also varies according to the facilit...

#### LU factorization

Form an LU factorization of the following symmetric matrix to show that it is not positive definite. 4 1 -1 2 1 3 -2 -1 -1 -2 1 6 2 -1 6 1 Using a little ingenuity we can find a non-zero vector such as x^T = ( 0 1 1 0) that does not satisfy the requirement x^T Ax > 0.

#### Non-Linear Scatterplot

See the attached file. An experiment is conducted to determine the relationship between initial speed and stopping distance of automobiles. A sample of twelve cars is tested and the following data are recorded: Initial speed in mph (x) 20 20 30 30 40 40 50 50 60 60 70 70 Stopping di...

#### Schedule Model

Suppose you are waiting in line to check out at a grocery store and there are 7 other customers in front of you (so you are customer 8). By inspecting the amount of items in their baskets, you estimate the following check-out time in minutes: Customer 1 2 3 4 5 6 7 8 Checkout time 10 5 ...

#### Calculating Production and Material Consumption Rates

The Ottawa Coat company manufactures winter coats and spring jackets. The winter coat requires 4m of material while the spring jacket requires just 1m. The company wants to minimize the consumption of material. Each winter coat has one zipper while each spring jacket has two. The seamstresses can se...

#### Isomorphisms Described

f(x)=x^3+x+1 and g(x)=x^3+x^2+1 are irreducible over F_2. K is the field extension obtained by adjoining a root of f and L is the extension obtained by adjoining a root of g. Determine the number of isomorphisms from K to L. (It is not necessary to explicitly describe such an isomorphism)

#### Properties of the Dihedral Group D8

Let D_8 denote the group of symmetries of the square. Denote by a a rotation anticlockwise by ?/2 about the centre of the square, and by b a reflection through the midpoints of an opposite pair of edges. (i) Verify that each rotation in D_8 can be expressed as a^i and each reflection can be expr...

#### ring and kernel

i. Let R be a set with 2 laws of composition satisfying all ring axioms except the comutative law for addition. Use the distributive law to prove that the commutative law for addition holds, such that R is a ring. ii. Find generator for the kernel of the map Z[x]->C defined by x->sqrt(2)+sqrt(3).

#### Structure of Rings

a) Determine the structure of the ring R obtained from Z by adjoining an element w satisfying each set of relations: (i) 2w-6=0, w-10=0 and (ii) w3+w2+1=0, w2+w=0. b) Let f=x4+x3+x2+x+1 and let y denote the residue of x in the ring R=Z[x]/(f). Express (y3+y2+y)(y5+1) in terms of the basis (1,y,y2,y...

#### Correspondence theorem

(a) The kernel of this homomorphism is the principal ideal (x-1). Therefore, Z[x]/(x-1) is isomorphic to Z. According to the correspondence theorem, ideals of Z[x]/(x-1) are in one-to-one correspondence with ideals of Z[x] containing (x-1). Taking into account the above-mentioned isomorphism, we o...

#### Problems in Galois Theory

a. Let K be a field of characteristic p > 0, and let c in K. Show that if alpha is a root of f (x) = x^p - x - c, so is alpha + 1. Prove that K(alpha) is Galois over K with group either trivial or cyclic of order p. b. Find all subfields of Q ( sqrt2, sqrt 3) with proof that you have them all. ...