Give a detailed example of a Resource-Allocation linear programming application model. Support whether the variables have to be integers for your example.

You are responsible for conducting a reliability sequential qualification test for a new keyboard design. The system MTBF requirement goal is 6,000 hours and the minimum acceptable MTBF is 4,000 hours. Both producer and consumer level of risk is 0.10, or 10%. If after 60,000 hours of testing, 20 failures are recorded, what do you recommend?

• A. Reject the system.
• B. Accept the system.
• C. There is insufficient data given to do an analysis and make a recommendation.
• D. Continue testing.

Use the Gram-Schmidt process to construct an orthogonal basis of the subspace of V = C ∞[0, 1] spanned by f(x) = 1, g(x) = x, and h(x) = e x where V has the inner product defined by < f, g >= R 1 0 f(x)g(x)dx.

Prove or disprove: two consecutive rotations about two different axis are commutative. That is, is RuRv = RvRu? (Hint: For simplicity, you can assume that the axis u is the x-axis and v is the y-axis without loss of gnerality).

Show your steps! The previous answer posted is wrong...could you do it again)

4. Three Plinko chips fall in such a way that each chip is equally likely to fall into any one of five slots. All chips may fall into the same slot or two may fall into the same slot or all three may fall into different slots. Let ? denote the number of unoccupied slots at the end of the game. What is the moment generating function of ??

Use the Lagrange multiplier method to identify the stationary point(s) of the function ?(?, ?, ?)=10? + 5? + ? + 2?^2 + 4?? + ?^2 + 2?? - ?^2 - ??, subject to the constraint 5? + 3? + ? = 27. Subsequently determine the nature of the stationary point(s) using the bordered Hessian matrix.

Company A and Company B are both wholly owned subsidiaries of Parent, Inc. Parent has no other operations, balance sheet items or income statement items other than its ownership of Company 1 (located in China) and Company 2 (located in US). Company 2 periodically sells goods to Company 1 for resale to end customers. Such goods are sold at the same pricing terms that Company 2 sells to all other customers. Prior to January 1, 2018, there had never been any inventory sales from Company 1 to Company 2 or from Company 2 to Company 1. The following is data for each company for 2018 and 2019:

Company 1 Company 2

     Year ended 12/31/18

Sales to all customers $300 million $150 million

Costs of sales $150 million $100 million

All other non production expenses $ 60 million $ 40 million

Pre tax income $ 90 million $ 10 million

Inventory purchased from Company 1 held

By Company 2 at end of year NONE

Inventory purchased from Company 2 held

By Company 1 at end of year $15 million

    Year ended 12/31/19

Sales to all customers $280 million $160 million

Costs of sales $140 million $120 million

All other non production expenses $ 60 million $ 30 million

Pretax income $ 80 million $ 10 million

Inventory purchased from Company 1 held

By Company 2 at end of year NONE

Inventory purchased from Company 2 held

By Company 1 at end of year $16 million

What would consolidated pretax income be for Parent for 2018 and 2019

Let S={1,2,3,6} and define the relation ~ on S² by (m,n) ~ (k,l) for m+l=n+k

1. Show that it is an equivalent relation
2. Find the number of different equivalent classes and write all of them

Let S = {1,2,3,4} and let A = SxS
Define a relation R on A by (a,b)R(c,d) iff ad = bc

Write out each equivalence class (by "write out" I mean tell me explicitly which elements of A are in each equivalence class)

Hint: |A| = 16 and there are 11 equivalence classes, so there are several equivalence classes that consist of a single element of A.

Prove a connected simple graph G with 16 vertices and 117 edges is not Eulerian.

3. Given the following maximum problem, set up the initial simplex tableau and circle the first pivot element.

Do not solve the maximum problems

MAXIMIZE : P = 3x1+2x2+3x3 subject to constraints : -x1+2x2+2x3<=8 4x1-x2+6x3<=10 x1+2x2+4x3<=12, x1>=0, x2>=0, x3>=0