Question

In: Advanced Math

Z X1 X2 X3 X4 X5 X6 RHS 1 170 0 0 25 -20 0 15,550...

Z X1 X2 X3 X4 X5 X6 RHS
1 170 0 0 25 -20 0 15,550
0 3 0 1 1/2 -1 0 65
0 1 1 0 0 1/2 0 205
0 -5 0 0 -1 2 1 480

a) Which variables are nonbasic, which ones are basic, and what are their respective values?

b) If I were minimizing the objective, which nonbasic variables are legitimate candidates to enter the basis? How about if I were maximizing?

c) Suppose I decided to enter x4 into the basis and increase its value by 100 units. Without doing any pivoting, can you say what the new objective value will be? Explain clearly.

d) Corresponding to this 100 unit increase in x4 what are the adjustments that need to be made to the values of the current basic variables in order to maintain feasibility? Explain clearly.

e) What is the maximum amount of increase possible in the value of x4? Explain clearly.

f) Again, without doing any pivoting, can you say what the value of the objective will be after the next iteration is completed?

Solutions

Expert Solution


Related Solutions

Let X1, X2, X3, X4, X5, and X6 denote the numbers of blue, brown, green, orange,...
Let X1, X2, X3, X4, X5, and X6 denote the numbers of blue, brown, green, orange, red, and yellow M&M candies, respectively, in a sample of size n. Then these Xi's have a multinomial distribution. Suppose it is claimed that the color proportions are p1 = 0.22, p2 = 0.13, p3 = 0.18, p4 = 0.2, p5 = 0.13, and p6 = 0.14. (a) If n = 12, what is the probability that there are exactly two M&Ms of each...
Case Y X1 X2 X3 X4 X5 X6 1 43 45 92 61 39 30 51...
Case Y X1 X2 X3 X4 X5 X6 1 43 45 92 61 39 30 51 2 63 47 73 63 54 51 64 3 71 48 88 76 69 68 70 4 61 35 86 54 47 45 63 5 81 47 85 71 66 56 78 6 43 34 51 54 44 49 55 7 58 35 70 66 56 42 67 8 71 41 64 70 57 50 75 9 72 31 81 71 69 72 82...
The values of X1, X2, X3, X4 and X5 are .1, .2, .08, .2 and .3....
The values of X1, X2, X3, X4 and X5 are .1, .2, .08, .2 and .3. Explicate the meaning of those numbers for the Z score. What are the prospects of this firm? Discuss thoroughly.
Let U = {(x1,x2,x3,x4) ∈F4 | 2x1 = x3, x1 + x4 = 0}. (a) Prove...
Let U = {(x1,x2,x3,x4) ∈F4 | 2x1 = x3, x1 + x4 = 0}. (a) Prove that U is a subspace of F4. (b) Find a basis for U and prove that dimU = 2. (c) Complete the basis for U in (b) to a basis of F4. (d) Find an explicit isomorphism T : U →F2. (e) Let T as in part (d). Find a linear map S: F4 →F2 such that S(u) = T(u) for all u ∈...
Using Y as the dependent variable and X1, X2, X3, X4 and X5 as the explanatory...
Using Y as the dependent variable and X1, X2, X3, X4 and X5 as the explanatory variables, formulate an econometric model for data that is (i) time series data (ii) cross-sectional data and (iii) panel data – (Hint: please specify the specific model here not its general form).
Use the following code fragment: 1       sub x4,x4,x0      2       add x3,x4,x0      3       sub x6,x3,x2...
Use the following code fragment: 1       sub x4,x4,x0      2       add x3,x4,x0      3       sub x6,x3,x2      4       mul x1,x6,x7      5       add x2,x5,x9      6       div x5,x9,x2      7       add x8,x1,x4 Draw the dependency graph among the instructions and indicate the type of data hazards (such as RAW, WAW, etc.) on each edge.
Let X1, X2, X3, X4, X5 be independent continuous random variables having a common cdf F...
Let X1, X2, X3, X4, X5 be independent continuous random variables having a common cdf F and pdf f, and set p=P(X1 <X2 <X3 < X4 < X5). (i) Show that p does not depend on F. Hint: Write I as a five-dimensional integral and make the change of variables ui = F(xi), i = 1,··· ,5. (ii) Evaluate p. (iii) Give an intuitive explanation for your answer to (ii).
4.Maximize: Z = 2X1+ X2-3X3 Subject to: 2X1+ X2= 14 X1+ X2+ X3≥6 X1, X2, X3≥0...
4.Maximize: Z = 2X1+ X2-3X3 Subject to: 2X1+ X2= 14 X1+ X2+ X3≥6 X1, X2, X3≥0 Solve the problem by using the M-technique.
Y1 Y2 X3 X4 X5 X6 X7 478 184 40 74 11 31 20 494 213...
Y1 Y2 X3 X4 X5 X6 X7 478 184 40 74 11 31 20 494 213 32 72 11 43 18 643 347 57 70 18 16 16 341 565 31 71 11 25 19 773 327 67 72 9 29 24 603 260 25 68 8 32 15 484 325 34 68 12 24 14 546 102 33 62 13 28 11 424 38 36 69 7 25 12 548 226 31 66 9 58 15 506 137 35...
The prices of inputs (x1,x2,x3,x4) are (4,1,3,2): (a) If the production function is given by f(x3,x4)...
The prices of inputs (x1,x2,x3,x4) are (4,1,3,2): (a) If the production function is given by f(x3,x4) =min⁡{x1+x2,x3+x4} what is the minimum cost of producing one unit of output? (b) If the production function is given by f(x3,x4)=x1+x2 +min⁡{x3+x4} what is the minimum cost of producing one unit of output?
ADVERTISEMENT
ADVERTISEMENT
ADVERTISEMENT