Lakeside Boatworks is planning to manufacture three types of molded fiberglass recreational boats $-$ a fishing $($bass$)$ boat, a ski boat, and a jet boat. The estimated selling price and variable cost for each type of boat are summarized in the following table:

The company has incurred fixed costs of $$2,800,000$ to set up its manufacturing operation and begin production.

Lakeside has also entered into agreements with several boat dealers in the region to provide a minimum of $70$ bass boats, $50$ ski boats, and $50$ jet boats.

Alternatively, the company is unsure of what actual demand will be$,$ so it has decided to limit production to no more than $120$ of any one boat.

The company wants to determine the number of boats that it must sell to break even while minimizing its total variable cost.

$\backslash$table$[[$Boat$,$Variable Cost,Selling Price$],[$Bass$,$$$12,500,$$$23,000$