Cane Company manufactures two products called Alpha and Beta that sell for $$195$ and $$150,$ respectively. Each product uses only one type of raw material that costs $$5$ per pound. The company has the capacity to annually produce $123,000$ units of each product. Its average cost per unit for each product at this level of activity are given below:

Alpha Beta

Direct materials $ $40$ $ $15$

Direct labor $3428$

Variable manufacturing overhead $2220$

Traceable fixed manufacturing overhead $3033$

Variable selling expenses $2723$

Common fixed expenses $3025$

Total cost per unit $ $183$ $ $144$

The company considers its traceable fixed manufacturing overhead to be avoidable, whereas its common fixed expenses are unavoidable and have been allocated to products based on sales dollars. $1.$ What is the total amount of traceable fixed manufacturing overhead for each of the two products? $2.$ What is the company$$s total amount of common fixed expenses? $13.$ Assume that Cane$$s customers would buy a maximum of $95,000$ units of Alpha and $75,000$ units of Beta. Also assume that the raw material available for production is limited to $245,000$ pounds. How many units of each product should Cane produce to maximize its profits?