Consider the modified version of "Design of Radiation Therapy" problem described in the lecture slides of Week 4. The linear programming (LP) model of this problem is given as: Minimize Z = 0.5X1 + 0.7x2 subject to: 0.3x1 + 0.1x2 s 2.7 0.5X1 + 0.5x2 = 6 0.6X1 + 0.4x2 2 6 0.8 X1 + 0.2x225 X12 0; X220 a) Solve the problem using AMPL by constructing only the ".mod" file. b) Solve the problem using AMPL by constructing the ".mod" and ".dat" files