Assume that Cane’s customers would buy a maximum of 96,000 units of Alpha and 76,000 units of Beta. Also assume that 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?

"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 are given below: Alpha Beta $ 21 Direct materials $42 Direct labor 35 28 Variable manufacturing overhead Traceable fixed manufacturing overhead Variable selling expenses 23 21 31 34 28 24 Common fixed expenses 31 26 $190 $154 Total cost per unit 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."

contribution margin per unit:

Alpha = $215 - $128 = $87

Beta = 160 - $94 = $66

pounds of raw materials per unit:

Alpha = $42 / $7 = 6

Beta = $21 / $7 = 3

since the production constraint is the number of pounds of raw materials available, the contribution margin per pound:

Alpha = $87 / 6 = $14.50

Beta = $66 / 3 = $22

so the company should try to produce the largest amount of betas as possible = 76,000 x 3 pounds = 228,000 pounds

remaining production of alphas = (246,000 - 228,000) / 6 = 3,000 units