Champions’ Shoes Ltd is a manufacturer of sport shoes, specialized in the production of basketball and soccer shoes. The Marketing Director of the company is about to draw the 2014/2015 plan for allocating the marketing resources to the sponsorship of basketball and soccer teams. Each soccer teams requires that 120 pairs of shoes must be provided whether sponsored, while each basketball team requires 32 pairs of shoes to be supplied. Furthermore, additional promotional and sponsorship costs include £ 150,000 for each sponsored soccer team and £ 225,000 for each sponsored basketball team. The overall monetary budget available to the Marketing Director for the sponsorship campaign is equal to £ 20,000,000. The production of promotional shoes for sponsoring teams is constrained to the availability of raw materials and in particular to the availability of a special gel used for branding shoes. Champions’ Shoes has 4,000 cm3 of gel available for the next 2014/2015 sponsorship campaign. Producing one pair of basketball shoes requires 3 cm3 of gel, while producing one pair of soccer shoes requires 1 cm3 of gel. The Marketing Director desires to find the maximum number of teams to be sponsored, constrained to the available monetary and production resources. You are required to help the Director to achieve this target by: a) Formulating the algebraic linear programming problem [35% of the marks of this Section] b) Solving the problem through the graphical method [30% of the marks of this Section] c) Formulating the linear programming problem on a spreadsheet and finding the optimal solution via the Solver [35% of the marks of this Section]

Cholesterol is an established risk factor for developing heart disease.   Among older age groups, men tend to have lower cholesterol than women on average but the same is not necessarily true for younger age groups.   The data provided is a sample of cholesterol levels from blood tests among university students under the age of 30.   The gender of each student is also recorded.  

1. Test whether, in this age group, there is a significant difference between the cholesterol for men and women.   In particular:

1. State the null and alternate hypothesis
2. Calculate the test statistic
3. State the p-value (accurate to four decimal places)
4. Should the null hypothesis be rejected?
5. What do you conclude regarding the cholesterol of men and women under the age of 30?

2. Find a 90% confidence interval for the mean cholesterol for women under 30 using the sample provided.   Show your workings and provide answers accurate to four decimal places.
3. Would the 90% confidence interval for the mean cholesterol for men under 30 be wider or narrower than your answer in b). Explain, without calculating the confidence interval.CholesterolGender

   174	Female
   177	Female
   178	Female
   178	Female
   179	Female
   180	Female
   180	Female
   182	Female
   182	Female
   182	Female
   183	Female
   184	Female
   184	Female
   185	Female
   185	Female
   185	Female
   186	Female
   187	Female
   188	Female
   188	Female
   189	Female
   189	Female
   190	Female
   190	Female
   190	Female
   191	Female
   192	Female
   192	Female
   193	Female
   193	Female
   194	Female
   195	Female
   195	Female
   195	Female
   197	Female
   197	Female
   197	Female
   197	Female
   198	Female
   198	Female
   198	Female
   199	Female
   199	Female
   201	Female
   202	Female
   174	Male
   180	Male
   181	Male
   182	Male
   186	Male
   187	Male
   187	Male
   188	Male
   188	Male
   188	Male
   188	Male
   189	Male
   189	Male
   189	Male
   190	Male
   190	Male
   191	Male
   191	Male
   192	Male
   192	Male
   193	Male
   193	Male
   194	Male
   194	Male
   194	Male
   194	Male
   195	Male
   195	Male
   196	Male
   196	Male
   196	Male
   197	Male
   198	Male
   198	Male
   198	Male
   199	Male
   199	Male
   199	Male
   200	Male
   202	Male
   203	Male
   204	Male
   204	Male
   205	Male
   207	Male

Use the power series method to solve the given initial-value problem. (Format your final answer as an elementary function.)

(x − 1)y'' − xy' + y = 0, y(0) = −7, y'(0) = 2 Use the power series method to solve the given initial-value problem. (Format your final answer as an elementary function.)

14.1.19 Find the future value of an annuity due with an annual payment of ​$11 comma 000 for three years at 3​% annual interest using the simple interest formula. How much was​ invested? How much interest was​ earned? What is the future value of the​ annuity? ​$ nothing ​(Round to the nearest cent as​ needed.) Enter your answer in the answer box and then click Check Answer. 2 parts remaining

New problem 14.1.23 Find the future value of a quarterly annuity due of ​$4 comma 100 for five years at 10​% annual interest compounded quarterly. How much was​ invested? How much interest was​ earned? LOADING... Click the icon to view the Future Value of​ $1.00 Ordinary Annuity table. The future value is ​$ nothing.​ (Round to the nearest cent as​ needed.) Enter your answer in the answer box and then click Check Answer. 1 part remaining

Let {Kn : n ∈ N} be a collection of nonempty compact subsets of R N such that for all n, Kn+1 ⊂ Kn. Show that K = T∞ n=1 Kn is compact. Can K ever be the empty set?

1. (5) Given the IVP xdy/dx- y = 2x^2;y (1) = 5: (a) Write the DE in standard form.
(b) Compute the integration factor, (x): Show your work.
(x) =
(c) Find the general solution of the DE. Show your work.
(d) Use the inital condition to solve for c: Show your work.
c =
(e) What is the largest interval I over which the solution is dened? Write your answer in the box.
2. (3) Given the DE (1 + y2 + xy2) dx + (x2y + y + 2xy) dy = 0:
(a) Show that the DE is exact.
(b) Find f (x;y): Show your work. Write your answer in the box.
f (x;y) =
(c) Find the solution. Write your answer in the box.
3. (2) Find an integrating factor for the inexact DE (xy2 2y3) dx + (32xy2) dy = 0: Show your work. Write your answer in the box.

use laplace transform to solve the initial value problem:

y''+4y=3sint y(0)=1, y'(0)=-1

On a circular array with n positions, we wish to place the integers 1, 2, ... r in order, clockwise, such that consecutive integers, including the pair (r,1) are not in adjacent positions on the array. Arrangements obtained by rotation are considered the same. In how many ways can this be done? Give a combinatorial proof.

1)

April wants $7,000 saved in 4 years to make a down payment on a house. How much money should she invest now at 3.15% compounded semiannually in order to meet her goal?

2)

How much will need to be invested at the beginning of every 2 months at 7.7% compounded every 2 months, to pay off a debt of $24,000.00 in 5 years?

The every 2 months payments are $. (Round to 2 decimal places.)

The community park has a small lake where visitors can rent paddle boats at $1 for 15 minutes, up to 2 hours. After 2 hours, the rate increases to $3 for 30 minutes.

Problem Write the piecewise function to model this situation and graph the function.

  1. What is the rental charge at 15 minutes? At 16 minutes? At 45 minutes?

2. If you had only $15, how long could you rent a boat?

3. How are the two lines in the graph the same, and how are they different?

4. How would the graph change if the rate change occurred at ? = 1 hour?

5. How would the graph change if the fee were $2 for 15 minutes?

6. What is the rental fee at 3 hours?

Paper trim problem: The Oblivion Paper Company produces rolls of paper for use in adding machines, desk calculators, and cash registers. The rolls, which are 200 feet long, are produced in widths of 1½, 2½, and 3½ inches. The production process provides 200-foot rolls in 10-inch widths only. The firm must therefore cut the rolls to the desired final product sizes. The five cutting alternatives and the amount of waste generated by each are as follows:

1 6 0 0 1

2 0 1 2 0.5

3 1 3 0 1

4 1 2 1 0

5 4 0 1 0.5

The minimum product requirements for the three products are as follows:

With the goal of minimizing the number of units of the 10-inch rolls will be processed on each cutting alternative, find each of the following:
Total Number of 10-inch Rolls Processed =

Note: Value is between 2485 and 2535

Number of 1½ inch rolls produced =

Number of 2½ inch rolls produced =

Number of 3½ inch rolls produced =

Number of Rolls Cut Using Alternative 1 =

Number of Rolls Cut Using Alternative 4 =

Number of Rolls Cut Using Alternative 5 =

*******Complete in Excel and show Formulas*******

Don't copy answers from other ones

it's different question Look carefully thanks

Describe the strings in the set S of strings over the alphabet Σ = {a, b, c} defined recursively

by (1) c ∈ S and (2) if x ∈ S then xa ∈ S and xb ∈ S and cx ∈ S.

Hint: Your description should be a sentence that provides an easy test to check if a given string is in the set or not. An example of such a description is: S consists of all strings of a’s, b’s, and c’s, with more a’s than b’s. That isn’t a correct description since cab is in S and doesn’t have more a’s than b’s, and also baac isn’t in S, but does have more a’s than b’s. So that attempted description is really terrible. The best way to do this problem is to use the rules to build a bunch of strings in S until a suitable description becomes obvious.

Q58 Describe the general approach by which analysis of variance is applied and the type of applications for which it is used. [3 Marks]

DO NOT WRITE THE ANSWER - USE WORD FORMAT.

NO PLAGIARISM IS ACCEPTED IN THE ANSWER

Q33 Answer the following questions:

(a) What is the primary difference between a periodic inventory system and a perpetual inventory system? [2 Marks]

(b) A company usually reports on different types of inventory. Elaborate these and explain how they are different. [2 Marks]

DO NOT WRITE THE ANSWERS - USE WORD FORMAT.

NO PLAGIARISM IN THE ANSWERS PLEASE