$31)$ Jersey Company owns a machine that can produce two specialized products. Production time for Product TLX is two hours per unit and for Product MTV is four hours per unit. $($Remember to convert units per hour to hours per unit.$)$ The machine's capacity is $14,500$ hours per year. Both products are sold to a single customer who has agreed to buy all of the company's output up to a maximum of $3,740$ units of Product TLX and $2,090$ units of Product MTV$.$ Selling prices and variable costs per unit to produce the products follow. Determine $(1)$ the company's most profitable sales mix and $(2)$ the contribution margin that results from that sales mix. See the Interactive Homework item number $5$ for the method on how to do this calculation.

$\backslash$table$[[,$Product TLX$,$Product MTV$],[$Selling price per unit,$$12\mathrm{.}10,$$$15\mathrm{.}90$