Dan's Danimal Palace needs a capacity plan for their critical operations. They manufacture three products: hammocks, cages and gift baskets. Each of these products uses a common machine in their production process. Below is a table of relevant information for each product.

$\backslash$table$[[$Product$,\backslash$table$[[$Annual$],[$Demand$]],\backslash$table$[[$Processing$],[$Time$],[($seconds$)]],\backslash$table$[[$Set$-$up$],[$Time$],[($seconds$)]],$Lot size$],[\backslash$table$[[$Cat$],[$Hammocks$]],367,143,86,95,301],[$Cat cages,$153,301,133,102,742],[\backslash$table$[[$Gift$],[$Baskets$],[($for cats$)]],174,896,86,178,106]]$

Dan's Danimal Palace operates two $8-$hours shifts, $7$ days a week, $48$ weeks per year $($a total of $19,353,600$ seconds over the year$).$ Dan has determined a capacity cushion of $6\%$ is sufficient. How many machines does Dan need to have to meet the company's processing needs?