I am needing help determining the : a. What is the profit if the traditional con

Question

I am needing help determining the :
a. What is the profit if the traditional contribution margin method is used for determining CKC's product mix?
b. What is the profit if the bottleneck method is used for determining CKC’s product mix?
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.

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 $10 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.
***Product A: $4 RM-- Step 1 Station W (10 min)--Step 2 Station X (10 min)-- Purchased Part $3-- Step 3 Station Y (15 min)-- Price: $60/unit Demand: 80units/wk
***Product B: $7 RM-- Step 1 Station X (20 min)--Step 2 Station W (14 min)--Purchased Part $8-- Step 3 Station Y (11 min)-- Price $85/unit Demand 85 units/wk

I am needing help determining the :
a. What is the profit if the traditional contribution margin method is used for determining CKC's product mix?
b. What is the profit if the bottleneck method is used for determining CKC’s product mix?
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.

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 $10 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.
***Product A: $4 RM-- Step 1 Station W (10 min)--Step 2 Station X (10 min)-- Purchased Part $3-- Step 3 Station Y (15 min)-- Price: $60/unit Demand: 80units/wk
***Product B: $7 RM-- Step 1 Station X (20 min)--Step 2 Station W (14 min)--Purchased Part $8-- Step 3 Station Y (11 min)-- Price $85/unit Demand 85 units/wk

I am needing help determining the :
a. What is the profit if the traditional contribution margin method is used for determining CKC's product mix?
b. What is the profit if the bottleneck method is used for determining CKC’s product mix?
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.

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 $10 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.
***Product A: $4 RM-- Step 1 Station W (10 min)--Step 2 Station X (10 min)-- Purchased Part $3-- Step 3 Station Y (15 min)-- Price: $60/unit Demand: 80units/wk
***Product B: $7 RM-- Step 1 Station X (20 min)--Step 2 Station W (14 min)--Purchased Part $8-- Step 3 Station Y (11 min)-- Price $85/unit Demand 85 units/wk

Explanation / Answer

a) Traditional method

Step 1: Compute bottleneck station

Aggregate workload of W = processing time for product A * demand rate of product A + processing time for product B * demand rate of product B

= 10*80 + 14*85 = 1990 minutes

Aggregate workload of X = 10*80 + 20*85 = 2500 minutes

Aggregate workload of Y = 15*80 + 11*85 = 2135 minutes

Available minutes = 40 hours per week * 60 minutes = 2400 minutes

Workstation X has the highest aggregate workload (2500 minutes, which is more than available capacity of 2400 minutes) and thus serves as the bottleneck for CKC.

Step 1: Compute contribution margin of each product

Contribution margin of product A = 60 - 4 - 3 = $ 53

Contribution margin of product B = 85 - 8 - 7 = $ 70

Product B has higher contribution margin. Therefore, product B should be prioritized.

Step 3: Determine optimal production mix

Remaining time on bottleneck station X after allocating 85 units of product B = 2400 - 85*20 = 700 minutes

Number of units of product A that can be produced = 700/10 = 70 units

Therefore, optimal weekly production mix = A = 70, B = 85

Weekly Profit = Contribution margin of product A and B - Labor cost - Overhead cost

= 70*53 + 85*70 - 3*40*10 - 3500

= $ 4960

b) Bottleneck method

Determine contribution margin per minute of bottleneck station processing time

Contribution margin per minute of bottleneck station processing time for Product A = 53/10 = 5.3

Contribution margin per minute of bottleneck station processing time for Product B = 70/20 = 3.5

Product A gives higher contribution margin per minute of bottleneck station processing time

Therefore, product A should be prioritized

Remaining time on bottleneck station X after allocating 80 units of product A = 2400 - 80*10 = 1600 minutes

Number of units of product B that can be produced = 1600/20 = 80 units

Therefore, optimal weekly production mix = A = 80, B = 80

Weekly Profit = Contribution margin of product A and B - Labor cost - Overhead cost

= 80*53 + 80*70 - 3*40*10 - 3500

= $ 5140

c. Profit gain, both in absolute dollars as well as in terms of percentage gains, by using TOC principles of determining product mix.

Profit gain in absolute dollars = 5140 - 4960 = $ 180

Profit gain in percentage = 180/4960 = 3.63 %

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