Set Up and Solve the Following Nonlinear Programming Problem Using

question 32

Essay

Set up and solve the following nonlinear programming problem using Excel:
$$\begin{array} { l } \operatorname { Max } : \left( \mathrm { X } _ { 1 } - 5 \right) ^ { 2 } + \left( \mathrm { X } _ { 2 } - 7 \right) ^ { 2 } \\\text { Subject to } \\\mathrm { X } _ { 1 } \leq 15 \\\mathrm { X } _ { 2 } \leq 15 \\\mathrm { X } _ { 1 } + \mathrm { X } _ { 2 } \geq 10 \\\mathrm { X } _ { 1 } , \mathrm { X } _ { 2 } \geq 0\end{array}$$

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Definitions:

Graded Bedding

A geological structure in which each layer of sediment is progressively heavier or finer, indicating deposition over time.

Water Current Velocity

The speed at which water flows in a specific direction in rivers, streams, or other bodies of water.

Sedimentary Sequence

A chronological order of sedimentary rocks laid down in layers, reflecting the history of sediment deposition over time.

Shale

A type of fine-grained sedimentary rock that splits into thin layers, formed from mud composed of clay and other minerals.