Part 3. Questions 3,4,5. [ Use Video-2 under Scheduling heading. ]

[Note: The order of jobs in a schedule ABCDE is 1^st,2^nd,3^rd,4^th,5^th, respectively.]

Five jobs arrived to be processed with the processing times and due dates.

. . .

2-Explain the dilemma of temperament.

Determine all values of a for which the following set of vectors is dependent or independent. You can select 'always', 'never', 'a = ', or 'a ≠', then specify a value or comma-separated list of values. ⎧ ⎪ ⎨ ⎪ ⎩⎫ ⎪ ⎬ ⎪ ⎭a001, 12−2−2, 48−8−9Dependent: When a = 0Independent: When a ≠ 0

Suppose you want to provide a general expression for the number of edges in a complete graph Kn. Explain how you could provide some examples to help you find a pattern. How can you use the pattern to create a formula?

from MATH-125

Use De Moivre’s Theorem to show

cos(3θ) = 4 cos^3 θ - 3 cos θ

Hence, obtain all solutions of x for the following equation

3x 4x^3 = 1.

Compare the monthly payments and total loan costs for the following pairs of loan options. Assume that both loans are fixed rate and have the same closing costs.

You need a ​$110,000 loan.

Option​ 1: a​ 30-year loan at an APR of 7.25​%.

Option​ 2: a​ 15-year loan at an APR of 6.8%.

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1.) Find the monthly payment for each option.

The monthly payment for option 1 is what?

The monthly payment for option 2 is​what?.

​(Do not round until the final answer. Then round to the nearest cent as​ needed.)

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Find the total payment for each option.

The total payment for option 1 is what?

The total payment for option 2 is what?

​(Round to the nearest cent as​ needed.)

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Compare the two options. Which appears to be the better​ option?

A. Option 2 is the better​ option, but only if the borrower can afford the higher monthly payments over the entire term of the loan.

B. Option 1 will always be the better option.

C. Option 1 is the better​ option, but only if the borrower plans to stay in the same home for the entire term of the loan.

D. Option 2 will always be the better option

1. Determine whether the relations described by the conditions below are reflexive, symmetric, antisymmetric or transitive on a set A = {1, 2, 3, 4}
   • All ordered pairs of (x, y) such that x   not Equal   y.
   • All ordered pairs of (x, y) such that y > 2.
   • All ordered pairs of (x, y) such that x = y ± 1.
   • All ordered pairs of (x, y) such that x = y².
   • All ordered pairs of (x, y) such that x > y².

margret measures the angle of elevation of the peak of a mountain as 35 degrees, doug who is 1200 feet closer on a straight level path, measures the angle of elevation as 42 degrees

1)) Sketch the picture. 2) Find the distance between margret and the peak. 3) Find the distance between doug and the peak. 4) How tall is the mountain?

1. A Scrap metal dealer has received a bulk order from a customer for a supply of at least 2000 kg of scrap metal. The consumer has specified that at least 1000 kgs of the order must be high quality copper that can be melted easily and can be used to produce tubes. Further, the customer has specified that the order should not contain more than 200 kgs of scrap which are unfit for commercial purposes. The scrap metal dealer purchases the scrap from two different sources in an unlimited quantity with the following percentages (by weight) of high quality of copper and unfit scrap

The cost of metal purchased from source A and source B are $12.50 and $14.50 per kg respectively. Determine the optimum quantities of metal to be purchased from the two sources by the metal scrap dealer so as to minimize the total cost. Formulate an LP model.

2. Company Z manufacture two products, model A and model B. Each unit of model A requires 2 kg of raw material and 4 labor hours for processing, whereas each unit of model B requires 3 kg of raw materials and 3 labor hours for the same type. Every week, the firm has an availability of 60 kg of raw material and 96 labor hours. One unit of model A sold yields $40 and one unit of model B sold gives $35 as profit. Formulate a Linear Programming model to determine as to how many units of each of the models should be produced per week so that the firm can earn maximum profit.

LINEAR PROGRAMMING MODEL

WITH SOLN PLS THANK YOU!

Verify the green theorem for:
P (x, y) = 2xy
Q (x, y) = x + y
C is the curve formed by the line segments from (0,0) to (3,0), from (3,0) to (2,1) and from (2,1) to (0,0)

For the line integral, you can solve through the parameterization analysis please

1. Zero Turbulence Airline provides air transportation services between Los Angeles, California; and Kona, Hawaii. A single Los Angeles to Kona round-trip flight has the following operating statistics: Fuel $14,062 Flight crew salaries 10,771 Airplane depreciation 5,087 Variable cost per passenger—business class 50 Variable cost per passenger—economy class 40 Round-trip ticket price—business class 530 Round-trip ticket price—economy class 260 It is assumed that the fuel, crew salaries, and airplane depreciation are fixed, regardless of the number of seats sold for the round-trip flight. If required round the answers to nearest whole number. a. Compute the break-even number of seats sold on a single round-trip flight for the overall product, E. Assume that the overall product is 20% business class and 80% economy class seats. Total number of seats at break-even seats b. How many business class and economy class seats would be sold at the break-even point? Business class seats at break-even seats Economy class seats at break-even seats

2. For a recent year, Wicker Company-owned restaurants had the following sales and expenses (in millions):

Assume that the variable costs consist of food and packaging, payroll, and 40% of the general, selling, and administrative expenses.

a. What is Wicker Company's contribution margin? Round to the nearest million. (Give answer in millions of dollars.)
$ million

b. What is Wicker Company's contribution margin ratio? Round to one decimal place.
%

c. How much would income from operations increase if same-store sales increased by $1,300 million for the coming year, with no change in the contribution margin ratio or fixed costs? Round your answer to the closest million.
$ million

Answer each question by True or False. Justify your answer.

(1) True or False? The set V = {p ∈ P2: p (7) = 0, p’ (7) = 0} is a subspace of P2.

(2) True or False? The set of 2 by 2 matrices whose entries are either all 0 or all nonzero is a subspace of the set of all 2 by 2 matrices M2×2(R).

(3) True or False? The set of all functions in C([0, 1]) such that f(0) = f( 1 /3 ) = f( 2 /3 ) = f(1) = 0 is a subspace. Note: C([0, 1]) is the set of continuous functions on [0,1].

(4) True or False? For an m × n matrix A, the null space is always a subspace of Rn.

(5) True or False? The set of all solutions to the ODE y’’ + 2y’ 0 +y = 3e^x forms a vector space.

(6) True or False? The ODE y’’ +2y’ +y = cos(e^x −7)+ sec(x) can be solved using the technique of undetermined coefficients.

Find a particular solution to the differential equation using the Method of Undetermined Coefficients.

x''(t)-2x'(t)+x(t)=96t^2e^t

8. Find the solutions of the following initial value problems

• x ''' + 6x '' + 12x ' + 8x = 0, x(1) = −2, x' (1) = x '' (1) = 0

• x ^(5) + 4x^ (4) + 5x^ (3) = 0, x(0) = x ' (0) = x '' (0) = 1, x^(3) (0) = x^ (4) (0) =0