David, LaDeana, and Lydia are the sole partners and workers in a company that produces fine clocks. David and LaDeana are each available to work a maximum of $40$ hours per week at the company, while Lydia is available to work a maximam of $20$ hours per week.

The company makes two different types of clocks: a grandfather clock and a wall clock. To make a clock, David $($a mechanical engineer$)$ assembles the inside mechanical parts of the clock while LaDeana $($a woodworker$)$ produces the hand$-$carved wood casings. Lydia is responsible for taking orders and shipping the clocks. The amount of time required for each of these tasks is sown next.

$\backslash$table$[[,$Time Required$],[$Task$,$Grandfather Clock,Wall Clock$],[$Assemble clock mechanism,$6$ hours,$4$ hours$],[$Carve wood casing,$8$ hours,$4$ hours$],[$Shpping$,3$ hours,$3$ hours$]]$

Each grandfather clock built and shipped yields a profit of $5300,$ while each wall clock yields a profit of $$200.$