An electronics manufacturer's new product uses four marketing distribution channels: marine, business, retail, and direct mail. Profitability of the product, advertising costs, and personal sales effort will vary with the distribution channel as shown below. The advertising budget is $$5000,$ and a maximum of $1800$ hours of sales force time is available. Management decided to produce exactly $600$ units. Finally, due to a contract, at least $150$ units need to be distributed through the national retail stores. The problem is to maximize the profitability of the new product.

$\backslash$table$[[,,,,\backslash$table$[[$Personal Sales$],[$Distribution Channel$]],\backslash$table$[[$Profit per Unit$],[$Sold $($$$)]],\backslash$table$[[$Advertising Cost$],[$per Unit Sold $($$$)]],\backslash$table$[[$Effort per Unit Sold$],[($hours$)]]],[$Marine Distributors,$90,10,2,,,,,],[$Business Distributors,$84,8,3,,,,,],[$National Retail Stores,$70,9,3,,,,,],[$Direct Mail,$60,15,0,,,,,]]$

On a separate piece of paper, formulate the problem.

What are the variables?