Cane Company manufactures two products called Alpha and Beta that sell for $130 and $90, respectively. Each product uses only one type of raw material that costs $5 per pound. The company has the capacity to annually produce 102,000 units of each product. Its average cost per unit for each product at this level of activity are given below: AlphaBetaDirect materials$ 25$ 10Direct labor2221Variable manufacturing overhead177Traceable fixed manufacturing overhead1820Variable selling expenses1410Common fixed expenses1712Total cost per unit$ 113$ 80 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 82,000 units of Alpha and 62,000 units of Beta. Also assume that the raw material available for production is limited to 162,000 pounds. How many units of each product should Cane produce to maximize its profits?