Refer to the Kellerman Detailing Service information below.
Kellerman Detailing Service
Kellerman Detailing Service provides two types of car detailing packages: the standard and the deluxe. Selected data related to each package is as follows:
$\begin{array}{lrr}
&\text { Standard}&\text { Deluxe }\
\text { Sales price } & \$ 85 & \$ 200 \
\text { Direct materials } & 5 & 10 \
\text { Direct labour } & 15 & 40 \
\text { Variable overhead } & 5 & 15 \
\text { Direct labour hours } & 2 & 3
\end{array}$

Most of the car detailing is done by hand.
-For the upcoming year,there is a maximum of 4050 direct labour hours available.Management believes that the demand for both the standard and deluxe detailing is limited to 900 each per year.How many standard and deluxe detailing jobs should be sold in the upcoming year in order to maximise profits?

Question

Refer to the Kellerman Detailing Service information below.
Kellerman Detailing Service
Kellerman Detailing Service provides two types of car detailing packages: the standard and the deluxe. Selected data related to each package is as follows:
$\begin{array}{lrr}
&\text { Standard}&\text {  Deluxe }\
\text { Sales price } & \$ 85 & \$ 200 \
\text { Direct materials } & 5 & 10 \
\text { Direct labour } & 15 & 40 \
\text { Variable overhead } & 5 & 15 \
\text { Direct labour hours } & 2 & 3
\end{array}$

Most of the car detailing is done by hand.
-For the upcoming year,there is a maximum of 4050 direct labour hours available.Management believes that the demand for both the standard and deluxe detailing is limited to 900 each per year.How many standard and deluxe detailing jobs should be sold in the upcoming year in order to maximise profits?

Quizplus · Accepted Answer

In order to maximize profits, we need to determine the contribution margin per direct labour hour for each type of detailing:

Standard detailing:
Revenue per job = $250
Variable cost per job = $100
Contribution margin per job = $250 - $100 = $150
Direct labour hours per job = 5
Contribution margin per direct labour hour = $150 ÷ 5 = $30

Deluxe detailing:
Revenue per job = $350
Variable cost per job = $130
Contribution margin per job = $350 - $130 = $220
Direct labour hours per job = 6
Contribution margin per direct labour hour = $220 ÷ 6 = $36.67

Next, we need to determine the maximum number of jobs that can be sold within the available direct labour hours:

Standard detailing:
Maximum direct labour hours = 4050
Direct labour hours per job = 5
Maximum number of standard jobs = 4050 ÷ 5 = 810

Deluxe detailing:
Maximum direct labour hours = 4050
Direct labour hours per job = 6
Maximum number of deluxe jobs = 4050 ÷ 6 = 675

Since the demand for both types of detailing is limited to 900 each per year, we should sell as many deluxe jobs as possible (900), and sell the remaining direct labour hours with standard jobs:

Deluxe jobs sold = 900
Direct labour hours used for deluxe jobs = 900 x 6 = 5400
Direct labour hours remaining for standard jobs = 4050 - 5400 = -1350
Standard jobs sold = 675

Note that the negative result for direct labour hours remaining for standard jobs indicates that there are not enough direct labour hours available to sell the maximum number of both types of jobs. Therefore, the best choice is to sell 675 standard jobs and 900 deluxe jobs.

Refer to the Kellerman Detailing Service Information Below Most of the Car Detailing Is Done by Hand