Solve the following linear fractional program:
max ? = ?1+2?2+?3+6/ 3?1+?3+5
s.t. ?1 + ?2 + 3?3 ≤ 10
2?1 + 3?2 ≤ 7
?1,?2,?3 ≥ 0
Let ? = 1/ 3?1+?3+5 and ?1 = ??1,?2 = ??2, ?3 =
??3.
Solve the following linear fractional program: max ? = ?1+2?2+?3+6/ 3?1+?3+5 s.t. ?1 + ?2 +...
Question 3 Solve the following linear program: Max 3x+2y s.t. 2x+2y <8 A 3x+2y < 12 B 1x+0.5y < 3C x,y> 0 w How much slack is in constraint B? 2 units of slack O 10 units of slack O 2 units of surplus 10 units of surplus
Consider the following linear fractional program (LFP):$$ \begin{array}{ll} \max f\left(x_{1}, x_{2}\right)= & \frac{10 x_{1}+20 x_{2}+10}{3 x_{1}+4 x_{2}+20} \\ \text { s.t. } \quad & x_{1}+3 x_{2} \leq 50 \\ & 3 x_{1}+2 x_{2} \leq 80 \\ & x_{1}, x_{2} \geq 0 \end{array} $$(a) Transform this problem into an equivalent linear program.(b) Use Matlab (or other software) to solve the LP you created in part (a).(c) Use your answer from part (a) to find a solution to the original LFP.(d) Does...
For the linear program Max 3 A + 3 B s.t. A + 2B ≤ 8 5A + 3B ≤ 15 A, B ≥ 0 Draw graph that identifies the optimal solution. What is the value of the objective function at the optimal solution?
Consider the following linear program: Max. 2A + 10B s.t. 3A ≤ 15 B ≤ 6 4A + 4B = 28 A, B ≥ 0 a.) Plot a graph that shows the feasible region for the problem b.) What are the extreme points of the feasible region
Consider the following linear program: Max 2A + 10B s.t. 3A ≤ 15 B ≤ 6 4A + 4B = 28 A, B ≥ 0 a. draw graph that shows the feasible region for the problem b. What are the extreme points of the feasible region c. Draw graph that shows the optimal solution for the problem
Solve the following linear program using the graphical solution procedure: (1) What are the value of A and B at each extreme point and (2) an optimal solution? Max 5 A + 7 B s.t (1) A <= 6 (2) 2 A + 3 B >= 18 (3) A + B <= 8 (4) A and B are Non-Negative
Let (IP) be the following integer program: max (0, -1). s.t. 1-1 -107 -10 10 -11</-0.5 1-10 / 0 z integer Let (LP) be the LP relaxation of (IP). We draw the feasible region of (LP) here. 2. . . . . . . to (LP), and prove that it is optimal by providing a (a) Determine an optimal solution certificate of optimality.
For the linear program Max 3A+2B s.t. A+B>=4 3A+4B<=24 A>=2 A-B<=0 A, B>=0 a. Write the problem in standard form. b. Solve the problem. c. What are the values of the slack and surplus variables at the optimal solution?
1. (20 pts.) Consider the following linear program: max 4x4 +xz+5x3 +3x4 s.t. *1 -X2 -X3 +3X, 51 5x +xz+3X3 +8X555 -X2 +2x2+3x3 -5x53 It is claimed that the solution x* = (0,14,0,5) is an optimal solution to the problem. Give a proof of the claim. Do not use the simplex method to solve this problem.
Consider the following all-integer linear program: Max x1+x2 s.t 4x1+6x2 <= 22 x1+5x2<= 15 2x1+x2<=9 x1,x2>=0 integer Solve in Excel Solver and AMPL.