Consider the following linear model. Маx z %3D 2x1 + X2 — Xз subject to X1 + 2x2 + x3 < bị -X1 + x2 – 2x3 < b2 X1, X2, Xз 2 0 The final simplex tableau was given below. X1 X2 X3 X4 X5 RHS 1 a b 3 d 16 X1 f 1 8 X5 h -1 1 1 12 a) Find the values of bị and bz. b) Fill in the missing values (a, b, ..., h) of the tableau. c) What is the reduced cost of x2? d) What are the shadow prices? Are there any free goods?

2. Solve the system of linear equation as follows: 2x1 + x2 4.x1 + 5x2 – 3x3 + 6x4 -2x1 + 5x2 – 2x3 + 6x4 4.x1+ 11x2 – 4.x3 + 8x4 x3 + 2x4 %3D 9 4 -

Derive and use 4 step-rule Show your solution in two questions: ( x+5 2 2 r¯ + 2 3 y= 3Vx+1 g(x) = and

A company produces two types of solar panels per year: x thousand of type A and y thousand of type B. The revenue and cost equations, in millions of dollars, for the year are given as follows. R(x,y) = 6x + 8y C(x,y)=x²-3xy + 6y² + 3x + 5y − Determine how many of each type of solar panel should be produced per year to maximize profit.

Match the property used in each equation to rewrite it. Group of answer choices X + Y + Z = Y + Z + X                                                                                                                                  12/4 + 3 = 3 + 4/12                                                                                                                                  (A+B)+C = A+(B+C)                                                                                                                                  -3(X + Y) = -3X - 3Y                                                                                                                                  (X)(Y)(Z) = (Y)(X)(Z)                                                                                                                                  (2/3) * (3/2) = 1

Q3 A- Find all solutions to this equation (Plot to get rough estimates) N^6 N^3=2 B- Find all solutions for the following system of equations (Hint: Plot) SQRT(x) - SQRT(y) = 17 x- y = 85 C- Find a solution to the following set of equations (using any method you like) -3.0X1 -1.1X2 -2.0X3 -1.8X4 = 1.0 3.2x1 + 2.1X2 +3.2X3 +5.2X4 = 2.0 3.4X1 +2.4X2 -4.2X3 +3.2X4 = 8.0 2.6X1 +2.1X2 -3X3 +3.4X4 = -5.0 How sensitive is the solution to the value in the right hand side of first equation (if it changes from 1 to 1.1, or to 0.9 how does the solution changes)