Cane Company manufactures two products called Alpha and Beta that sell for $195 and $150, respectively. Each product uses only one type of raw material that costs $5 per pound. The company has the capacity to annually produce 123,000 units of each product. Its unit costs for each product at this level of activity are given below Alpha Beta
Direct materials $40 $15
Direct labor 34 28
Variable manufacturing overhead 22 20
Traceable fixed manufacturing overhead 30 33
Variable selling expenses 27 23
Common fixed expenses 30 25
Total cost per unit $183 $144
The company considers its traceable fixed manufacturing overhead to be avoidable, whereas its common fixed expenses are deemed unavoidable and have been allocated to products based on sales dollars.
1) What contribution margin per pound of raw material is earned by Alpha and Beta?
2) Assume that Cane's customers would buy a maximum of 95,000 units of Alpha and 75,000 units of Beta. Also, assume that the company's raw material available for production is limited to 245,000 pounds. How many units of each product should Cane produce to maximize its profits?
3) Assume that Cane's customers would buy a maximum of 95,000 units of Alpha and 75,000 units of Beta. Also, assume that the company's raw material available for production is limited to 245,000 pounds. What is the maximum contribution margin Cane Company can earn given the limited quantity of raw materials?
4) Assume that Cane's customers would buy a maximum of 95,000 units of Alpha and 75,000 units of Beta. Also, assume that the company's raw material available for production is limited to 245,000 pounds. Up to how much should it be willing to pay per pound for additional raw materials?

Explanation:

Alpha = $195

Beta = $150

total production capacity = 123,000 pounds

raw materials = $5 per pound

Production costs per unit                        Alpha                Beta

direct materials                                          $40                   $15

direct labor                                                 $34                   $28

variable manufacturing overhead            $22                   $20  

fixed manufacturing overhead                 $30                   $33

variable selling expenses                         $27                   $23

common fixed expenses                          $30                   $25  

total cost per unit                                     $183                  $144

1) What contribution margin per pound of raw material is earned by Alpha and Beta?

                                                                Alpha                Beta

contribution margin                                  $72                  $64

contribution margin per pound               $9                  $21.33

2) Assume that Cane's customers would buy a maximum of 95,000 units of Alpha and 75,000 units of Beta. Also, assume that the company's raw material available for production is limited to 245,000 pounds. How many units of each product should Cane produce to maximize its profits?

                                                                Alpha                Beta

contribution margin                                  $72                  $64

contribution margin per pound                $9                  $21.33

production (in units)                                2,500              75,000

profits                                                    $30,000          $450,000

total profits                                                   $480,000

3) Assume that Cane's customers would buy a maximum of 95,000 units of Alpha and 75,000 units of Beta. Also, assume that the company's raw material available for production is limited to 245,000 pounds. What is the maximum contribution margin Cane Company can earn given the limited quantity of raw materials?

                                                                Alpha                Beta

contribution margin                                  $72                  $64

contribution margin per pound                $9                  $21.33

production (in units)                                2,500              75,000

contribution margin                             $180,000      $4,800,000

total contribution margin                            $4,980,000

4) Assume that Cane's customers would buy a maximum of 95,000 units of Alpha and 75,000 units of Beta. Also, assume that the company's raw material available for production is limited to 245,000 pounds. Up to how much should it be willing to pay per pound for additional raw materials?

If it wants to increase the production of Alpha, it could pay as much as ($195 - $183) / 8 = $1.50 extra per pound if it wants to maximize profits. Maximum price = $6.50 per pound. At this point, marginal revenue = price.