Imagine your company has $3$ products: TVs$,$ Stereos and Speakers. The profit is $$100$ per TV$,$ $$30$ per Stereo and $$30$ per Speaker.

Each of these products uses the same $5$ parts $($but in different amounts$)$: Chassis, Picture Tube, Speaker Cone, Power Supply and Electronics.

You have a total of $450$ Chassis, $250$ Picture Tubes, $900$ Speaker Cones, $450$ Power Supplies, and $600$ Electronic parts.

One TV uses $1$ Chassis, $1$ Picture Tube, $2$ Speaker Cones, $1$ Power Supply and $2$ Electronic Parts.

One Stereo uses $1$ Chassis, $0$ Picture Tube, $2$ Speaker Cones, $1$ Power Supply and $1$ Electronic Part.

One Speaker uses $1$ Chassis, $0$ Picture Tubes, $1$ Speaker Cone, $0$ Power Supply and $1$ Electronic Part.

Based on this information, please calculate the optimal product mix that would maximize profitability,

while not exceeding inventory constraints.

We'll use Excel's computing power $($with the solver algorithm$)$ to help...