Problem $7$:

$20$ Points

Mony Music manufactures three components for analog stereo systems: turn tables, tape decks,

and stereo turners. They are an "old school" component company. The wholesale price and

manufacturing costs of each item are shown in the following table:

Each turn table requires $3$ hours of assembly, each tape deck requires $2$ hours of assembly, and

each stereo turner requires $1$ hour of assembly. The marketing department has indicated that the

company can sell no more than $150,000$ turn tables, $100,000$ tape decks, and $90,000$ stereo tuners.

However, the demand is expected to be at least $50,000$ units of each component, and Mony Music

wants to meet this demand. If Mony Music has $400,000$ hours of assembly hours, how many of

each component should Mony Music product to maximize profit.