Problem $1$

Kelson Sporting Equipment, Inc. makes two different types of baseball gloves: a regular model and a catcher's model. The firm has $900$ hours of production time available in its cutting and sewing department, $300$ hours available in its finishing department, and $100$ hours available in its packaging and shipping department. The production time requirements and profit contribution per glove are given in the following table.

$(1)$ What is the optimal solution based on this data?

$(2)$ What is the total profit contribution Kelson can earn with the given production quantities?