Question

The senior management at Davis Watercraft would like to determine if it is possible to improve firm profitability by changing their existing product mix. Currently, the product mix is determined by giving resource priority to the highest contribution margin watercraft. Davis Watercraft always has a contingent of 10 workers on hand; each worker is paid $25 per hour. Overhead costs are $35,000 per week. The plant operate 18 hours per day and 6 days per week. Labor is considered a fixed expense because workers are paid their time regardless of their utilization. The production manager has determined that workstation 1 is the bottleneck. Detailed production information is given below.

	Model
	A	B	C
Price	$450	$400	$500
Material Cost	$50	$40	$110
Weekly Demand	100	75	40
Processing Time Station 1	60 min	0 min	30 min
Processing Time Station 2	0 min	0 min	60 min
Processing Time Station 3	10 min	60 min	0 min
Processing Time Station 4	20 min	30 min	40 min

1. Using the traditional method, the product mix that yields the highest total profit is (_____) units of product A, (_______),   units of product B, and (____) units of product C.

2. Using the bottleneck method, the product mix that yields the highest total profit is(_____) units of product A, (____) units of product B, and (____) units of product C.

3.

The weekly profit in the bottleneck-based method is(______) dollars.

Answer 1

1) Using traditional method,

Profit of model A = 450-50 = $ 400

Profit of model B = 400-40 = $ 360

Profit of model C = 500-110 = $ 390

Production is scheduled in order of profits of each model. So, production priority is: A, C, B

Workload of station 1 = 100*60+75*0+40*30 = 7200 min

Workload of station 2 = 100*0+75*0+40*60 = 2400 min

Workload of station 3 = 100*10+75*60+40*0 = 5500 min

Workload of station 4 = 100*20+75*30+40*40 = 5850 min

Available time per workstation per week = 6*18*60 = 6480 min.

Workload of station 1 is greater than available time. So, station 1 is the bottleneck.

Available time after production of 100 units of A = 6480 - (100*60 = 480

Production of C = 480/30 = 16 units

Production mix: A = 100, B = 75, C = 16

Highest total profit = Profit from 3 models - overhead cost - labor cost

= 100*400+75*360+16*390-35000-10*40*25 (labor cost is calculated considering 40 hours of labor per worker per week)

= $ 28,240

Using the traditional method, the product mix that yields the highest total profit is (_100__) units of product A, (__75__),   units of product B, and (__16__) units of product C.

2) Using bottleneck method,

Profit of model A per minute of bottleneck station 1 = (450-50)/60 = $ 6.67

Profit of model B per minute of bottleneck station 1 = (400-40)/0 = infinity

Profit of model C per minute of bottleneck station 1 = (500-110)/30 = $ 13

Production is scheduled in order of profits per minute of bottleneck time of each model. So, production priority is: B, C, A

Available time after production of 75 units of B and 40 units of C = 6480 - (75*0+40*30) = 5280

Production of A = 5280/60 = 88 units

Production mix: A = 88, B = 75, C = 40

Highest total profit = Profit from 3 models - overhead cost - labor cost

= 88*400+75*360+40*390-35000-10*40*25 (labor cost is calculated considering 40 hours of labor per worker per week)

= $ 32,800

Using the bottleneck method, the product mix that yields the highest total profit is (_88_) units of product A, (__75__),   units of product B, and (__40__) units of product C.

3) The weekly profit in the bottleneck-based method is (__32,800__) dollars