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(Solved): 3. First, solve the following problem using linprog () routine of MATLAB. \[ \begin{array}{ll} \te ...
3. First, solve the following problem using linprog () routine of MATLAB. \[ \begin{array}{ll} \text { Maximize } & x_{1}+2.5 x_{2} \\ \text { subject to } & x_{1}+3 x_{2} \leq 10 \\ & 3 x_{1}+x_{2} \leq 12 \\ & 0.5 x_{1}+x_{2} \geq 1 \\ & x_{1}, x_{2} \geq 0 \end{array} \] Then, solve it using MATLAB's intlinprog () routine for which the second variable is real-valued, but the second variable can only take an integer value. Explain, why the second solution is worse than the first solution in terms of its function value? See 'Module 1, Lecture 2, Part 5 - Existing Search and Optimization Methods: Matlab Opt. Codes 2 (pdf)' on the use of linprog () and intlinprog () routines.
Expert Answer
Hi, Given that, (i) linprog method : comments are incoporated in code for better understanding MATLAB CODE : clear all; close all; A = [1 3 ; 3 1 ; -0.5 -1]; % coefficients of x1 and x2 in "subject to inequality constraints made AX <= b" b = [10 ;