Cane Company manufactures two products called Alpha and Beta that sell for $$210$ and $$172,$ respectively. Each

product uses only one type of raw material that costs $$8$ per pound. The company has the capacity to annually

produce $128,000$ units of each product. Its average cost per unit for each product at this level of activity is given

below:

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.

Assume Cane's customers would buy a maximum of $98,000$ units of Alpha and $78,000$ units of Beta. Also assume the raw material

available for production is limited to $248,000$ pounds. How many units of each product should Cane produce to maximize its profits?