1. For each of the following linear programming models, give your recommendation on which is the more efficient way (probably) to obtain an optimal solution: by applying the simplex method directly to this primal problem or by applying the simplex method directly to the dual problem instead. Explain. (a) Maximize Z = 10x₁ - 4x₂ + 7x3 subject to 3x1x₂ + 2x3 ≤ 25 x12x2 + 3x3 ≤ 25 5x₁ + x₂ + 2x3 ≤ 40 x₁ + x₂ + x3 ≤ 90 2x₁x₂ + x3 ≤ 20 and x₁ ≥ 0, x₂ ≥ 0, x3 ≥ 0. (b) Maximize Z = 2x₁ + 5x₂ + 3x3 + 4x4 + x5 subject to 3x₁ + 3x₂ + 2x3 + 3x4 + x5 ≤6 4x₁ + 6x₂ + 5x3 + 7x4 + x5 ≤ 15 and x; ≥ 0, for j = 1, 2, 3, 4, 5.

An investor has $621,000 to invest in bonds.  Bond A yields an average of 8% and the bond B yields 7%.  The investor requires that at least 5 times as much money be invested in bond A as in bond B.  You must invest in these bonds to maximize his return.  This can be set up as a linear programming problem.  Introduce the decision variables: x= dollars invested in bond Ay= dollars invested in bond B Compute x+y. $                       .  Round to the nearest cent.   Investor Matt has $152,000 to invest in bonds.  Bond A yields an average of 9.2% and the bond B yields 8.4%.  Matt requires that at least 4 times as much money be invested in bond A as in bond B.  You must invest in these bonds to maximize his return.  What is the maximum return? $                       per year.  Round to the nearest cent.   Investor Dan has $607,000 to invest in bonds.  Bond A yields an average of 8.5% and the bond B yields 8.4%.  Dan requires that at least 4 times as much money be invested in bond A as in…

Solve the linear programming problem by the simplex method. Maximize  P = 16x + 13y subject to  x  +  y ≤  12 3x  +  y ≤ 30 10x  +  7y ≤ 70 x ≥ 0, y ≥ 0 The maximum is P =  at  (x, y) =                .

Solve the linear programming problem by the simplex method. Minimize 5x + y subject to the constraints shown on the right. The minimum value of Mis (Type integers or fractions.) which is attained for x = and y = x + y2 3 4x ≥ 11 x20, y20