Question: Minimize ( Z=40 X_{1}+50 X_{2} ) Subject to : [ begin{array}{ll} 2 X_{1}+3 X_{2} geq 30 & text { (resource } 1) X_{1}+X_{2} geq

$Minimize \$ Z=40 X_{1}+50 X_{2} \$ Subject to : \\[ \\begin{array}{ll}$

Minimize \$ Z=40 X_{1}+50 X_{2} \$ Subject to : \\[ \\begin{array}{ll} 2 X_{1}+3 X_{2} \\geq 30 & \\text { (resource } 1) \\\\ X_{1}+X_{2} \\geq 12 & \\text { (resource 2) } \\\\ 2 X_{1}+X_{2} \\geq 20 & \\text { (resource 3) } \\\\ X_{1}, X_{2} \\geq 0 & \\end{array} \\] a. Solve this problem by using graphical method. b. Find the range of \$ c_{1} \$ (coefficient of objective function \$ x_{1} \$ ) such that remain the optimal solution

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