$1.$ Performing an Optimization Analysis

Perform the analysis noted and be sure all questions are answered completely and professionally. Do not use abbreviated or incomplete sentences when responding.

Lion$-$Com Electronics manufactures five different models of telecommunications interface cards for PCs and laptops. As noted in the table below, each of these devices requires different amounts of printed circuit board, resistors, memory chips, and assembly.

Per Unit Requirements

HyperLink FastLink SpeedLink MicroLink EtherLink

Printed Circuit Board $($sq$.$ in$.)20151085$

Resistors $2824181116$

Memory Chips $88446$

Assembly Labor $($hours$)0\mathrm{.}750\mathrm{.}70\mathrm{.}50\mathrm{.}651$

The unit wholesale price and manufacturing cost for each model are as follows:

Per Unit Revenues and Costs

HyperLink FastLink SpeedLink MicroLink EtherLink

Wholesale Price $$189$ $$148$ $$129$ $$169$ $$139$

Manufacturing Cost $$139$ $$103$ $$92$ $$137$ $$105$

For the next production period, Lion$-$Com has $80,000$ square inches of PC board, $100,000$ resistors, $30,000$ memory chips, and $5,000$ hours of assembly time available. The company can sell all the product it can manufacture, but the marketing department warns to be sure the company produces at least $500$ units of each product and at least twice as many FastLink cards as HyperLink cards while maximizing profit.

As the company$$s analyst, please respond to the following providing details for each.

a$.$ Formulate the Linear Programming $($LP$)$ model for this problem and provide below:

b$.$ Input the LP model into Excel Solver and create an optimization run to generate the required result set. $($Note: Will create an Excel workbook that you can input the LP model: see examples from discussion videos$).$

c$.$ Provide the optimal solution for all decision variables $($show each below$)$ and what the objective function value is from the model run.