1. Consider the LP Max z=c1x1+2x2+c3x3
Subject to x1 + 5x2+a1x3 ≤ b1
X1-5x2+a2x3≤ b2
X1, x2, x3 ≥ 0
The optimal tableau for this LP is

Without using the simplex method, determine all unknown constants in this problem
(i.e., a1,a2,b1,b2, c1, c3, d1,d2, d3, d4)

2. Consider the following problem:
Maximize z= 6x1 + 8x2
Subject to 5x1 + 2x2 less than or equal to 20
x1 + 2x2 less than or equal to 12
x1, x2 greater than or equal to 0
(a) Sketch the feasible set and solve the program geometrically
(b) Determine all the basic solutions for this program and indicate them on the sketch in (a). Which ones are feasible? (there are 6 basic solutions, not all feasible).
(c) Solve the program by the simplex method. For each tableau, indicate which feasible solution corresponds to it
(d) Write the dual of this program. For each primal basic solution, determine the corresponding dual basic solution that satisfies the complementary slackness principle. Which ones are dual feasible?

3. Consider the system of equations -x1+x2-x3=3, -x1+2x2-x4=2, and x1+x2+x5=2
(a) by converting the equations into inequalities in two variables, show geometrically that there are no nonnegative solutions to this system.
(b) use the simplex method to show the same thing

4. Use the Karush-Kuhn conditions to solve:
Maximize z=2x1+x2+3x3
Subject to x1+2x2+x3 less than or equal to 12
X1,x2,x3 greater than or equal to 0

Verify that x^=(1,3) is a K_T point of the following problem.
Min f(x,y)=(x-1.5)^2+(y-5)^2
st.
g1(x,y)=-x+y<=2
g2(x,y)=2x+3y<=11
g3(x,y)=-x<=0
g4(x,y)=-y<=0

I have been trying to solvethe following problem.
Maximize z=x-y
subject to: x^2+y^2<=1
The attached file has the work I have done so far. I can't seem to reach plausible solutions.

How do you understand the term paradigm? What Kuhn mean by this term? Identify a paradigm in your particular discipline, if there is one. Why is this concept important to the study of research?

14-7. Tucker Lighting Company sells lamps and other lighting fixtures. The purchasing department manager prepared the following inventory purchases budget. Tucker Lighting's policy is to maintain an ending inventory balance equal to 10 percent of the following month's cost of goods sold. April's budgeted cost of goods sold is $8

250 words not counting citation:
Select one passage from one theorist in Critical Theory and explain to us what you understand it to mean.
Or, on the other hand, explain what you find confusing about such a passage.

Suppose that it is possible to provide internet backbone capacity at a constant marginal capital investment of $5 per megabit per second (mb/s). There are no marginal costs. There are two time periods during the day (for simplicity each will be 12 hours): day and night. During the peak period (daytime) of 250 business days p

Which philosophers of science philosophies are useful in the discipline of nursing practice and leadership? Justify/explain position for each.
Peer review citations/references are appreciated.

If you were to write about how to improve American society today, would you have a critical theory--that is, a theory about how to evaluate and judge it?
(Briefly, what would your theory be?)
Would criticism about so-called corporate culture be criticized on the same principles?