Canine Kennels Company (CKC) manufactures two different types of dog chew toys (
ID: 390307 • Letter: C
Question
Canine Kennels Company (CKC) manufactures two different types of dog chew toys (A and B, sold in 1,000-count boxes) that are manufactured and assembled on three different workstations (W, X, and Y) using a small-batch process (see the figure below). Batch setup times are negligible. The flowchart denotes the path each product follows through the manufacturing process, and each product's price, demand per week, and processing times per unit are indicated as well. Purchased parts and raw materials consumed during production are represented by inverted triangles. CKC can make and sell up to the limit of its demand per week; no penalties are incurred for not being able to meet all the demand. Each workstation is staffed by a worker who is dedicated to work on that workstation alone and is paid $77 per hour. Total labor costs per week are fixed. Variable overhead costs are $3,500/week. The plant operates one 8-hour shift per day, or 40 hours/week.
The senior management is concerned with the existing capacity limitation, so they want to accept the mix of orders that maximizes the company's profit. Traditionally, CKC has utilized a method whereby decisions are made to produce as much of the product with the highest contribution margin as possible (up to the limit of its demand), followed by the next highest contribution product, and so on until no more capacity is available. Because capacity is limited, choosing the proper product mix is crucial. Troy Hendrix, the newly hired production supervisor, is an avid follower of the theory of constraints philosophy and the bottleneck method for scheduling. He believes that profitability can indeed be improved if bottleneck resources are exploited to determine the product mix.
a. What is the profit if the traditional contribution margin method is used for determining CKC's product mix?
The profit with the traditional approach is $________(Enter your response rounded to the nearest whole number.)
b. What is the profit if the bottleneck method is used for determining CKC’s product mix?
The profit with the new bottleneck approach is $____ (Enter your response rounded to the nearest whole number.)
c. Calculate the profit gain, both in absolute dollars as well as in terms of percentage gains, by using TOC principles of determining product mix.
Profit increases by $______(Enter your response as an integer) which is a percentage gain of ______%(Enter your response as a percent rounded to two decimal places).
Product A Step 1 Station WW (11 min) Step 2 Station X (10 min) Step 3 Station Y (14 min) Product: A Price: $60/unit Demand: 90 units/wk $5 Raw materials Purchased pa Product B Step 1 Station X (20 min) Step 2 Station WW (10 min) Step 3 Station Y (11 min) Product: B Price: $85/unit Demand: 85 units/wk $7 Raw materials $9 Purchased partExplanation / Answer
Number of workers per workstation =1
# of workstations = 3
Available time per workstation per week = 40 hours x 60 minutes = 2400 minutes
Time per unit (in minutes)
Workstation
Product A
Product B
W
11
10
X
10
20
Y
14
11
Demand (units/week)
90
85
Determining Aggregate Workload for each WS:
Workload per product = demand x time per unit
Workstation
Load from Product D
Load from Product SD
Total Workload
(mins)
W
90 x 11 = 990
850
1840
X
900
1700
2600
Y
1260
935
2195
As the aggregate workload of WS-X is more than 2400 minutes, the WS-X is bottleneck WS.
Determine Contribution Margin per unit per product:
Product
A
B
Price
$60.00
$85.00
Raw Materials
$5.00
$7.00
Purchased Parts
$4.00
$9.00
Total material Cost
$9.00
$16.00
Contribution margin
60 – 9= $51
$69
PART A.
Product Mix according to Traditional Method:
Select the best product mix according to the highest overall contribution margin of each product.
Order of production schedule: B – A
Product Mix:
Select the best product mix according to the highest overall contribution margin of each product.
Since CM of item B is more than A, the order of production schedule is B – A
Product Mix:
First determine minutes remaining at all WS after producing 85 units of product B. Since WS-X is bottleneck process, determine units of item A can be produced with remaining time available on WS-X.
Time available on WS-X = 700 units
Unit processing of item A on WS-X = 10 mins
Units of Item A to be produced on WS-X = 700 mins/10 mins/unit = 70 units
Workstation
Minutes at start
Minutes left after making 85 units of B
Minutes left after making 70 units of A
W
2400
2400-850
= 1550
780
X
2400
700
0
Y
2400
1465
485
Product Mix: A – 70 units and B – 85 Units
Product
A
B
Total
Contribution margin/unit
$51
$69
Production units
70
85
Total Contribution margin
$3570
$5865
$9,435
Wages
3 workers x 40 hours x $8/hour
($840)
OH cost
($3,500)
Total profit
$5,095
Total Profit by Traditional contribution margin method = $5,095
Product Mix: A = 70 units and B = 85 units
PART b.
Product Mix according to Bottleneck Method:
Select the best product mix according to the dollar contribution margin per minute of processing time at the bottleneck workstation X. This method would take advantage of the principles outlined in the theory of constraints and get the most dollar benefit from the bottleneck.
Select the best product mix according to the highest overall contribution margin per minute of each product.
Product
A
B
Contribution margin
$51
$69
Time at bottleneck (mins)
10
20
Contribution margin per minute
$51/10 = $5.1
$69/20
= $3.45
Order of production schedule: A – B
First determine minutes remaining at all WS after producing 90 units of product A. Since WS-X is bottleneck process, determine units of product B can be produced with remaining time available on WS-X.
Time available on WS-X = 1500 units
Unit processing of item B on WS-X = 20 mins
Units of Item A to be produced on WS-X = 1500 mins/20 mins/unit = 75 units
Workstation
Minutes at start
Minutes left after making 90 units of A
Minutes left after making 70 units of A
W
2400
1410
660
X
2400
1500
0
Y
2400
1140
315
Product Mix: A – 90 units, B– 75 Units
Profitability of production plan:
Product
A
B
Total
Contribution margin/unit
$51
$69
Production units
90
75
Total Contribution margin
$4,590
$5,175
$9,765
Wages
3 workers x 40 hours x $8/hour
($840)
OH cost
($3,500)
Total profit
$5,605
b. The profit with the new bottleneck approach is $5,605
C.
Profit increase = Profit by traditional method – TOC method = $5,605 - $5,095 = $510
% increase in profit = profit increase/profit by traditional method = $510/$5,095 x 100 = 10%
Profit increase = $510
% increase in profit = 10.01%
Time per unit (in minutes)
Workstation
Product A
Product B
W
11
10
X
10
20
Y
14
11
Demand (units/week)
90
85
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