Question

Limited Resource Decisions

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

Answer 1

When there is limiting factor , then we should allocate and produce that product which yields more contribution per such constraint.

In the given case. , Constraint is labour hours and so we should calculate contribution per labour hour based on which we can allocate the limiting factor resources.

So . In the given case, Product C is contributing more labour hour and since there is no demand constraint for product C, we can allocate all the available labour hours to Product C.

This combination yields the Maximum Contribution and no other combination will give such contribution.

So , whatever the analysis given is correct.

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