A firm has prepared the following binary integer program to evaluate a number of potential locations for new warehouses. The firm’s goal is to maximize the net present value of their decision while not spending more than their currently available capital.

Max 20x1 + 30 x2 + 10x3 + 15x4

s.t. 5x1 + 7x2 + 12x3 + 11x4 ≤ 21 {Constraint 1}

x1 + x2 + x3 + x4 ≥ 2 {Constraint 2}

x1 + x2 ≤ 1 {Constraint 3}

x1 + x3 ≥ 1 {Constraint 4}

x2 = x4 {Constraint 5}

x j ={ 1, if location j is selected 0, otherwise xj=1, if location j is selected0, otherwise

Solve this problem to optimality and answer the following questions:

A. What is the net present value of the optimal solution? (Round your answer to the nearest whole number.)

B. How much of the available capital will be spent (Hint: Constraint 1 enforces the available capital limit)? (Round your answer to the nearest whole number.)

a. Seek power series solutions of the given differential equation about the given point x0; find the recurrence relation that the coefficients must satisfy.

b. Find the first four nonzero terms in each of two solutions y1 and y2 (unless the series terminates sooner).

y''-xy'-y=0 ; x0=0

A 1-kg mass stretches a spring 20 cm. The system is attached to a dashpot that imparts a damping force equal to 14 times the instantaneous velocity of the mass. Find the equation of motion if the mass is released from equilibrium with an upward velocity of 3 m/sec.

SOLVE THIS USING MATLAB CODE (SECOND ORDER DIFFERENTIAL EQUATIONS)

SOLVE THIS USING MATLAB CODE (SECOND ORDER DIFFERENTIAL EQUATIONS)

SOLVE THIS USING MATLAB CODE (SECOND ORDER DIFFERENTIAL EQUATIONS)

SOLVE THIS USING MATLAB CODE (SECOND ORDER DIFFERENTIAL EQUATIONS)

SOLVE THIS USING MATLAB CODE (SECOND ORDER DIFFERENTIAL EQUATIONS)

SOLVE THIS USING MATLAB CODE (SECOND ORDER DIFFERENTIAL EQUATIONS)

SOLVE THIS USING MATLAB CODE (SECOND ORDER DIFFERENTIAL EQUATIONS)

SOLVE THIS USING MATLAB CODE (SECOND ORDER DIFFERENTIAL EQUATIONS)

Fibonacci numbers are defined by F0 = 0, F1 = 1 and Fn+2 = Fn+1 + Fn for all n ∈ N ∪ {0}.

(1) Make and prove an (if and only if) conjecture about which Fibonacci numbers are multiples of 3.
(2) Make a conjecture about which Fibonacci numbers are multiples of 2020. (You do not need to prove your

conjecture.) How many base cases would a proof by induction of your conjecture require?

y� � y � 2x sin x

y'+xy=x³+y²    Solve the differential equation.

Answer the following questions.
(a) What is the implication of a correlation matric not being positive-semidefinite?
(b) Why are the diagonal elements of a correlation matrix always 1?
(c) Making small changes to a positive-semidefinite matrix with 100 variables will have no effect on the matrix. Explain this statement?

Solve this Initial Value Problem using the Laplace transform:

x''(t) - x'(t) - 6x(t) = e^(4t),

x(0) = 1, x'(0) = 1

QUESTION ONE

1.1  Use any appropriate method to integrate ∫2x^4(x^2-5)^50 dx [8]

1.2. Differentiate f(x) = loga x from the first principle .[9]

1.3 Find the binomial expansion for sqrt(x^2 - 2x) up to 3 terms for which values of x is the expansion valid? [10]

1.4 Given that z = x + jy, express z=2x - jy in terms of z and or z modulus in a simplest form. [6]

solve using variation of perameters

y'''-16y' = 2

Use Laplace transformations to solve the following ODE for x(t):

x¨(t) + 2x(t) = u˙(t) + 3u(t)

u(t) = e^−t

Initial conditions

x(0) = 1, x˙(0) = 0, u(0) = 0

Given the integral 1/x dx upper bound 2 lower bound 1

(a) use simpson's rule to approximate the answer with n=4

Formula:f(x)=1/3[f(x0)+4f(x1)+2f(x2)+...+f(xn)]Δx(keep answer to 6 decimals)

b)how large is n in order for the error of Simpsons rule for the given integral is no more than 0.000001

Formula: |Es|=(k)(b-a)^5/(180 n^4), where |f^4(x)≤k|

please show all work and steps

The following observations were obtained when conducting a two-way ANOVA experiment with no interaction.

a. Calculate SST, SSA, SSB, and SSE. (Round intermediate calculations to at least 4 decimal places. Round your answers to 2 decimal places.)

b. Calculate MSA, MSB, and MSE. (Round intermediate calculations to at least 4 decimal places. Round your answers to 2 decimal places.)

c. Construct an ANOVA table. (Round intermediate calculations to at least 4 decimal places. Round "SS", "MS" to 2 decimal places, "F" 3 decimal places.)

d. At the 1% significance level, do the levels of Factor B differ?

• Yes, since we reject the null hypothesis.

• No , since we reject the null hypothesis.

• Yes, since we do not reject the null hypothesis.

• No, since we do not reject the null hypothesis.

e. At the 1% significance level, do the levels of Factor A differ?

• Yes, since we reject the null hypothesis.

• No, since we reject the null hypothesis.

• Yes, since we do not reject the null hypothesis.

• No, since we do not reject the null hypothesis.

For the function, supply a valid technology formula.

r(x) = 30 (1 + 1/3.8)^4x

30*(1 + 1/3.8)^(−4*x)

30*(1 + 1/3.8)^(4*x)   

30*(1 + 1/3.8)*(4*x)

30*(1 + 3.8)*(4*x)

30*(1 + 3.8)^(−4*x)

Then use technology to compute the missing values in the table accurate to four decimal places.

Solve the following IVPs and determine the interval of validity of the solution.

(i)y′ = √1+x2 , y(0)=1

(ii)y′ =e−y(x−2), y(4)=0