Set Up and Solve the Following Nonlinear Programming Problem Using

Essay

Set up and solve the following nonlinear programming problem using Excel:
$$\begin{array} { l } \text { Max: } \mathrm { X } _ { 1 } + 2 \mathrm { X } _ { 2 } + 3 \mathrm { X } _ { 1 } \mathrm { X } _ { 2 } + 5 \mathrm { X } _ { 3 } 3 \\\text { Subject to } \\\mathrm { X } _ { 1 } + \mathrm { X } _ { 2 } + \mathrm { X } _ { 3 } \leq 75 \\\mathrm { X } _ { 1 } + \mathrm { X } _ { 2 } \geq 15 \\2 \mathrm { X } _ { 1 } + 2 \mathrm { X } _ { 3 } \leq 40 \\\mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } , \mathrm { X } _ { 3 } \geq 0\end{array}$$