Consider the following linear program:

   MAX Z = 25A + 30B

   s.t. 12A + 15B ≤ 300

   8A + 7B ≤ 168

10A + 14B ≤ 280

   Solve this linear program graphically and determine the optimal quantities of A, B, and the    value of Z. Show the optimal area.

You are given two containers, the first containing one litre of wine and the second one litre of water. You also have a cup which has a capacity of r litres, where 0 < r < 1. You fill the cup from the first container and transfer the content to the second container, stirring thoroughly afterwards. Next, dip the cup in the second container and transfer r litres of liquid back to the first container. This operation is repeated again and again. Prove that as the number of iterations n of the operation tends to infinity, the concentrations of wine in both containers tend to equal each other.

Write matlab program to compute ∫f(x)dx lower bound a upper bound b using simpson method and n points. Then, by recomputing with n/2 points and using richardson method, display the exact error and approximate error. (Test with a=0 b=pi f(x)=sin(x))

tate, with an​ explanation, whether the​ mean, median, or mode gives the best description of the following average. The average number of times that people change jobs during their careers

Provide a professional application of one multichannel queuing model. In addition, please provide a one paragraph description to the application and a one paragraph conclusion to the application.

Provide a professional application of one multivariate simulation model (avoid a Monte Carlo analysis. In addition, please provide a one paragraph description to the application and a one paragraph conclusion to the application.

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Problem from Hamilton Cycle Chapter: "Four married couples met at a restaurant for dinner every Friday night for three weeks. Sometimes a large table was available to accommodate all 8 people, but other times the group had to be divided across two smaller tables each with at least 3 seats. Nobody moved to a different seat during a meal, no married couple ever sat next to one another, and no two people sat next to one another for more than one dinner. On the first Friday the eight people sat at one table.

(a) Show that the group could have sat at 2 tables with 4 seats each for both the second and third Friday.

(b) Show that the group could have sat at 2 tables with 4 seats each for the second Friday and at 2 tables, one with 3 seats and the other with 5 seats, on the third Friday.

(c) Show that the group could have sat at 2 tables, one with 3 seats and the other with 5 seats, for both the second and third Friday.

(d) Show that the group could have sat at a table for 8 for the second Friday and any of 3 different table combinations on the third Friday.

Provide all working out and justification of all steps taken to reach the answer."

Now that you have conducted a series of inferential statistics to validate your claim. Discuss any three (3) possible concerns in business or statistical aspects regarding the approach used here. Such that in retrospect, how would you have done this study differently again?

1. Prove that any continuous function on a standard n-dimensional cube In can be uniformly approximated by polynomials in n variables x1, . . . , xn.

1) Consider the statement: “If it snows then we will stay home”. Find the:

Converse

Inverse

Contra-positive

Assuming the original statement is true, which statements must also be true?

Determine if the statement is true or false and provide a counter-example for the false statements.

The sum of two integers is an integer.

Prime numbers are odd.

The product of two irrational numbers is irrational.

The sum of a rational number and an irrational number is irrational.

Suppose that there are n people in a group, each aware of a different secret no one else in the group knows about. These people communicate by phone; when two people in the group talk, they share information about all secretes each knows about. For example, on the first call, two people share information, so by the end of the call, each of them knows about two secretes. The gossip problem asks for the number of phone calls that are needed for all n people to learn about all the secrets.

(a) Find the smallest number of telephone calls when there are 3 and 4 people respectively. [2 marks]

(b) Prove by induction that the total number of phone calls for all n people to learn about all secretes is not more than 2n−4 for any n ≥ 4.

Can somebody write down a biography of Euler for me please with two citing sources. Thanks.

PLEASE DONT COMMENT OR ANSWER IF YOU DON'T HAVE THE ANSWER.

Can somebody make a simple yet thorough explanation of Russell’s Paradox. It should contains the definition, explaining it, and as if you are teaching someone who has never heard of Russells paradox and include an example problem of it. Thanks.

23. Consider the 5 x 6 matrix A whose (i,j)h element is aij i+j;

(a) What is A(10:20)?

(b) What is k such that A(k) = A(3,4)?

(c) Show how A is stored in sparse column format

(d) Show how A is stored in sparse row format

(e) What is the sparsity ratio?