Question: Convert into a maximization problem and then solve each problem using both the dual method and the method of section 4.4. You may use an applet or something from the internet to help you, but you must explain each step. If you have it worked without an explanation for each step, you will receive no credit.

\(\begin{aligned} & Minimize:w=20{{y}_{1}}+15{{y}_{2}}+18{{y}_{3}} \\ & subject\,\,to:2{{y}_{1}}+{{y}_{2}}+{{y}_{3}}\ge 112 \\ & {{y}_{1}}\,\,\,\,+{{y}_{2}}+{{y}_{3}}\ge 80 \\ & {{y}_{1}}\,\,\,\,+{{y}_{2}}\,\,\,\,\,\,\,\,\,\,\,\ge 45 \\ & with{{y}_{1}}\ge 0,\,\,{{y}_{2}}\ge 0,\,\,{{y}_{3}}\ge 0 \\ \end{aligned}\)

Dual method: