Surf Company can sell all of the two surfboard models it produces, but it has only $456$ direct labor hours available. The Glide model requires $2$ direct labor hours per unit. The Ultra model requires $4$ direct labor hours per unit. Contribution margin per unit is $$256$ for Glide and $$412$ for Ultra.

$($a$)$ Compute the contribution margin per direct labor hour for each product.

$($b$)$ Determine the best sales mix and the resulting contribution margin.