stuck on level 4

The production-line employees at GE work four days a week, 10 hours a day. Each day of the

week, (at least) the following numbers of line employees are needed: Monday–Friday, 7 employees; Saturday and Sunday, 3 employees. GE has 11 production-line employees. Formulate an LP that can be used to maximize the number of consecutive days off received by the employees.

For example, a worker who gets Sunday, Monday, and Wednesday off receives two consecutive days off

I'm having trouble laying out this problem.

I have Xi days of the week ie X1 = Monday X2= Tuesday and Yj number of employees

and i know some of the constraints are

Yj > = 4 Employees work 4 days a week

X1 to x5 >= 7 at least 7 employees are needed Monday to Friday

X6 to x7 >= 3 at least 3 employees are needed Saturday and Sunday

but I'm not sure where to go from here especially with the objective function.

I'm using an open solver to solve the LP

Any tips or solutions would be handy.

so i have 1/(x+iy+1) but i have to get the answer in the form 1/((1+x)^2+y^2)+ x/((1+x)^2+y^2) -(i y)/((1+x)^2+y^2)

i'm noty sure how to do this, can anyone show working?

thanks

Differential equations aren't my strong point.

I have a general idea on how to solve this equation but help would be appreciated.

dy/dx = 1.6y - 0.2y^2 -3 with initial condition y(0)=60

i know you can multiply by 5 to make it easier and then use an integrating factor?

Hello Everyone,

This is my first attempt at this type of question but there's a few mistakes in my answer. If anyone could possibly help find out why? Any help would be appreciated.

Consider a rod of length 40cm, of a material for which a^2 =1. The ends of the rod are

maintained at 0 C
for all t > 0 . Find the temperature U ( x, t ) in the rod if the initial

temperature distribution is given by

(a) U ( x,0) = 50, 0 < x < 40

my answer: 100 + ∑ -200(cos((pi*n - 1) / (pi*n) ))*(e^(-n^2 * pi^2 * t /1600) - sin((n*pi) / 40)

right answer: 100/pi + ∑ (1-cos((pi*n ) / (n) )*(e^(-n^2 * pi^2 * t /1600) - sin((n*pi) / 40)

Not quite sure what to do here, do i multiply them together. My notes aren't descriptive or helpful in the slightest.

Suggest an alternative form of the function f(x)=sqrt(900+x)-30 that avoids loss of significance errors for small values of x.

The question after that is the same but 1-cos(x^2) is the function, would the process of solving it be the same?

Any help would be appreciated. Thank you.

Solve the complex matrix equation:

[1, j, 0; 0, 1, 0; 1, 0, j] X = [0; 1; 0]

where ; symbolize a new row

Please show working as I have no idea on how to proceed in answering this question. Any explanations are appreciated.

Do I take the inverse or something ?

The answer is [-j; 1; j]

Thanks in advance.

I have some random questions to do with vectors but an explanation of how to do the following is not included in my notes.

Can someone please explain how to get the correct answer.

It would be greatly appreciated.

Thanks in advance.

The length of the space curve

r(t) = 3t2 i + 2t3 j + 4t k

between P(3,2,4) and Q(12,16,8)

A ∫ (from 1 to 2) of (3t2 i + 2t3 j + 4t k) dt

B ∫ (from 1 to 2) of (6t i + 6t2 j + 4 k) dt

C ∫ (from 1 to 2) of (36t2 + 36t4 + 16) dt

D ∫ (from 1 to 2) of (9t4 + 4t6 + 16t2) dt

The position of a moving particle at time t is given by

r(t) = 2t3 i + t2 j + (2t + 1) k.

At the point P(16,4,5) this particle has velocity

A 30

B 1536i + 8j + 2k

C 24i + 4j + 2k

Each front tire on a particular type of vehicle is supposed to be filled to a pressure of 26 psi. Suppose the actual air pressure in each tire is a random variable - X for the right tire and Y for the left tire, with a joint probability density function of:

f(x,y)= 3/380,000 (x^2+y^2) 20≤x≤30, 20≤y≤30 0 otherwise

The part of this question I'm having trouble working out is :

What is the probability that the difference in air pressure between the two tires is at most 2 psi?

Thanks in advance.

Please help with the integral of of 5sin(cos(5x))*sin(5x) and show working.

One more question: how do you choose the appropriate method (substitution or use by parts rule) when solving one of these equations? ie: how do you know which one is better to use?

Thanks in advance.

I'm doing a proof my mathematical induction and I've gotten to a point and I know what the answer is but I don't know how its factorised to get there. Please show working / or an explanation as to why.

(1/3)k(k+1)(k+5)+(k+1)(k+4)

I know it equals (1/3)(k+1)(k+2)(k+6) but how did they reach this point?

f(x): arctan(arcsin(arctan(x)))

Find first derivative.

Please help, this question has been driving me crazy.