Consider the following all-integer linear program. Max 1x1 + 1x2 s.t. 5x1 + 7x2 ≤ 42 1x1 + 5x2 ≤ 20 2x1 + 1x2 ≤ 15 x1, x2 ≥ 0 and integer (b)Solve the LP Relaxation of this problem. ( ) at (x1, x2) = ( )
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Max | 1x1 | + | 1x2 | |
s.t. | ||||
5x1 | + | 7x2 ≤ | 42 | |
1x1 | + | 5x2 ≤ | 20 | |
2x1 | + | 1x2 ≤ | 15 | |
x1, x2 ≥ 0 and integer |
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- Show that any 2 *2 matrix A that does not have aninverse will have det A= 0.Let A = {0, 1, 2, 3} and define a relation R on A as follows: R = {(0, 0), (0, 2), (0, 3), (2, 2), (2, 0), (1, 1), (2, 1), (3, 3)}. (a) Draw the directed graph of R. (b) Is R reflexive? Explain. (c) Is R symmetric? Explain. (d) Is R transitive? Explain. Consider the following linear programming problem: Maximize 12X + 10Y Subject to: 4X + 3Y = 480 2X + 3Y 360 all variables 20 Which of the following points (X,Y) is not feasible? a (70,70) b. (20,90) c. (100,10) d. (0,100) كلا أجرب الأرقام بالـؤال
- Aa6. please solve with formulas not excellFor minimization linear programming problem, the simplex method is terminated when all values of: a. Z (NB) s0 Ob. None of them Z (NB) = 0 Z (NB) 2 0For the remaining questions, consider the following problem description: An oil company is considering exploring new well sites S₁, S2, ..., S10 with respective costs C1, C2, C10. And in particular they want to find the least-cost selection of 5 out of the 10 possible sites. The binary decision variables x₁,x2,..., X10 denote the decision to explore the corresponding site.
- Suppose we are solving a maximization problem andthe variable xr is about to leave the basis.a What is the coefficient of xr in the current row 0?b Show that after the current pivot is performed, thecoefficient of xr in row 0 cannot be less than zero.c Explain why a variable that has left the basis on agiven pivot cannot re-enter the basis on the next pivot.Consider an ARIMA(2,1,1) process. Write out the resulting model usinga. Backshift notation with the backshift operator B.b. Backshift notation with the operatorc. No backshift notationSolve the following linear programming problem. Maximize: z=6x + 14y subject to: 7x+3y ≤21 9x+y≤21 x20, y 20 The maximum value is The maximum occurs at the point (Type an ordered pair. If the maximum occurs at more than one point, type either answer. Type an integer or a fraction.)
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