Cane Company manufactures two products called Alpha and Beta that sell for $$215$ and $$160,$ respectively. Each product uses only one type of raw material that costs $$7$ per pound. The company has the capacity to annually produce $125,000$ units of each product. Its average cost per unit for each product at this level of activity is given below:

Alpha Beta

Direct materials $ $42$ $ $21$

Direct labor $3528$

Variable manufacturing overhead $2321$

Traceable fixed manufacturing overhead $3134$

Variable selling expenses $2824$

Common fixed expenses $3126$

Total cost per unit $ $190$ $ $154$

The company$$s traceable fixed manufacturing overhead is avoidable, whereas its common fixed expenses are unavoidable and have been allocated to products based on sales dollars.

$13.$ Assume Cane$$s customers would buy a maximum of $96,000$ units of Alpha and $76,000$ units of Beta. Also assume the raw material available for production is limited to $246,000$ pounds. How many units of each product should Cane produce to maximize its profits?