Luxury Auto Care Company offers three different service packages (A, B, and C) to its customers. These packages vary from a complete detailing of the automobile (wash, wax, carpet shampoo, etc.) to a simple hand wash. A limitation of 120 labor hours per week prevents Luxury from meeting the demand for its services. Information for the three service packages is as follows:

                                             A         B        C

Unit selling price                $100    $80    $50
Unit variable costs               (60)     (35)    (25)
Unit contribution margin   $ 40     $45      $25
Hours per unit                       4          3          1

Package A has the highest selling price and Package B has the highest unit contribution margin. Package Cis shown here to have the highest contribution per hour.

                                             A      B       C

Unit contribution margin   $40    $45    $25
Hours per unit                    : 4     : 3     : 1
Contribution per hour        $10     $15   $25

Following the rule of maximizing the contribution per unit of a constraining factor, Luxury should use its limited labor hours to sell Package C. As shown in the following analysis, any other plan would result in lower profits:

                                      A               B                       C
                                      Highest     Highest              Highest       
                                      Selling       Contribution     Contribution
                                      Price          Per Unit            Per
                                      Per Unit                              Constraining Factor
Hours available                120              120               120
Hours per unit                  :   4              : 3                  : 1
Weekly production-
in units                               30                40               120
Unit contribution margin x$40            x $45         x $25
Total weekly-
contribution margin          $1,200        $1,800        $3,000