Recall that the firm has $850$ ?hours of production time available in its cutting and sewing department, $200$ ?hours available in its finishing department, and $100$ ?hours available in its packaging and shipping department. The production time requirements and the profit contribution per glove are given in the following table. Model Production Time

$($ hours $)$

Cutting and Sewing Finishing Packaging and

Shipping Profit $/$ Glove

Regular model $1$ ?

$1$

$2$

$1$

$8$

$ $8$

Catcher's model

$3$

$2$

$1$

$3$

$1$

$4$

$ $9$