Benoit Company produces three products—A, B, and C. Data concerning the three products follow (per unit): Product
A B C
Selling price $80 $56 $70
Variable expenses:
Direct materials 24 15 9
Other variable expenses 24 27 40
Total variable expenses 48 42 49
Contribution margin $32 $14 $21
Contribution margin ratio 40% 25% 30%
The company estimates that it can sell 1,000 units of each product per month. The same raw material is used in each product. The material costs $3 per pound with a maximum of 6,600 pounds available each month. What is the maximum contribution margin that the company can earn per month if it makes optimal use of its 5,000 pounds of materials?

Solution :

A    ()                  $ 24        $ 15      $9

B    (Material cost per pound)                 $3            $3       $3

C=A/B (pound of material per unit)          8             5          3

D   (Contribution margin per unit)          $32         $14       $21

E=D/C (Contribution margin pound       $ 4           $ 2.8    $ 7

           of raw materials)

Order of preference to allocate material  2nd     3rd       1st

Since the product C has maximize 'contribution margin per pound' it will give 1st preference, followed by the product A and B.

The allocation of the available 5000 pounds of the raw material.

                                                                    A              B               C

Maximize units that can be sold (A)        1000         1000         1000  

Materials required per unit (B)                  8                5                3

Total material requirement (C)                 8000       5000         3000

Available raw material in pounds             5000 pounds

(-) first allocation to product C                   3000 pounds

Remaining material                                     2000 pounds

(-) seconds allocation to product A          2000 pounds

Remaining for the product B                        0 pounds

Now calculating the total contribution on the above allocation basis.

                                                               A          B                  C            Total

Material allocated to A(pounds)      2000        0                 3000      5000

Contribution per pound (B)                $ 4        $2.8                $7

Total contribution margin (AxB)      $8000     $0               $21000     $29,000

Therefore, the total contribution margin is $29,000.

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