The following linear programming problem is presented:

The company Astondoa, produces three kinds of motor yachts for water sports: type $1,$ type $2$ and type $3.$

$-$ Producing the type $1$ motor yacht requires $16$ tons of steel, $2$ tons of carbon fiber and $2$ tons of fiberglass and generates a profit of US$$33,000.$

$-$ Producing the type $2$ motor yacht requires $14$ tons of steel, $3$ tons of carbon fiber and $3$ tons of fiberglass and generates a profit of US$$35,000.$

$-$ Producing the type $3$ motor yacht requires $12$ tons of steel, $5$ tons of carbon fiber, and $3$ tons of fiberglass and generates a profit of US$$37,000.$

The company's production plant has a maximum of $600$ tons of steel, $150$ tons of carbon fiber, and $150$ tons of fiberglass.

Astondoa's financial management needs to optimize the profits received for each type of motor yacht and asks the production management to evaluate the optimal quantity of each type of motor yacht to be produced in order to optimize resources.

Formulate the Primal problem

Formulate the Dual problem and transform to its standard form.

Solve by the Dual Simplex Method

Interpret the dual variables of the obtained solution for the optimization of resources.