Cane Company manufactures two products called Alpha and Beta that sell for $185 and $150, respectively. Each product uses only one type of raw material that costs $8 per pound. The company has the capacity to annually produce 119,000 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 $24

Direct labor 33 28

Variable manufacturing overhead 20 18

Traceable fixed manufacturing overhead 28 31

Variable selling expenses 25 21

Common fixed expenses 28 23

Total cost per unit $174 $145

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.

13. Assume that Cane's customers would buy a maximum of 93,000 units of Alpha and 73,000 units of Beta. Also assume that the raw material available for production is limited to 227,000 pounds. How many units of each product should Cane produce to maximize its profits?