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Hello dear tutor, I have a long question. Even though I try every time, I cannot understand the process. Could you please explain it to me in a simple way? I would really appreciate it.
Sweet Treats Bakery makes three types of cake: brownies, muffins and cupcakes. The costs,
revenues and demand for each of the three cakes are as follows:
………………………………………Brownies …………..Muffins ………….Cupcakes
Batch size (units) ……………….. 40……………………30…………………..20
Selling price ($ per unit) ……. 1,5 …………………. 1,4 …………………..2
Material cost ($ per unit) ….. 0,25 ……………….. 0,15 ………………. 0,25
Labour cost ($ per unit) ……. 0,40 ……………….. 0,45 ………………. 0,50
Overheads ($ per unit) …….. 0,15 ………………… 0,20 ………………. 0,30
Minimum daily demand (units)..30………………..20……………………10
Maximum daily demand (units)..140………………90…………………..100The minimum daily demand is required for a long-term contract with a local café and must
be met.The cakes are made in batches using three sequential processes: weighing, mixing and
baking. The products must be produced in their batch sizes but are sold as individual units.
Each batch of cakes requires the following amount of time for each process:
………………………………………Brownies ……….Muffins ………….Cupcakes
Weighing (minutes) ………….. 15…………………15…………………..20
Mixing (minutes) ……………….. 20……………….. 16…………………..12
Baking (minutes) ……………… 120……………….. 110………………. 120The baking stage of the process is done in three ovens which can each be used for eight hours
a day, a total of 1,440 available minutes. Ovens have a capacity of one batch per bake,
regardless of product type.
Sweet Treats Bakery uses throughput accounting and considers all costs, other than material,
to be ‘factory costs’ which do not vary with production.QUESTION:
On Wednesday, the mixing process is identified as the bottleneck process. On this day,
only 120 minutes in the mixing process are available.
Assuming that Sweet Treats Bakery wants to maximise profit, what is the optimal
production plan for Wednesday?A) 80 brownies, 30 muffins and 100 cupcakes
B) 0 brownies, 90 muffins and 100 cupcakes
C) 120 brownies, 0 muffins and 100 cupcakes
D) 40 brownies, 60 muffins and 100 cupcakesThe mixing process is the bottleneck with only 120 minutes available, we need to analyse the throughput of each product and the time required for mixing. Follow a process with throughput:
1. Batch Sizes & Mixing Time
2. Throughput Calculation
3. Throughput per Minute
4. Ranking by Throughput per Minute
5. Production Plan
6. Maximising Remaining Time
7. Final Optimal Production Plan
Thus, the optimal production plan for Wednesday
is A) 80 brownies, 30 muffins, and 100 cupcakes.Batch Sizes and Mixing Times:
B take 20 m per b of 40 units
M 16 m per b 30 u
C 12 m per b 20 uThroughput Calculation:
B 1.50 – (0.25 + 0.40 + 0.15) = 0.70
M 1.40 – (0.15 + 0.45 + 0.20) = 0.60
C 2.00 – (0.25 + 0.50 + 0.30) = 0.95Throughput per Minute:
B 0.70 / 20 = 0.035
M 0.60 / 16 = 0.0375
C 0.95 / 12 = 0.0792Ranking by Throughput per Minute:
* C, M, BProduction Plan:
To maximise profit, we should first meet the minimum demand:
1 batch of C (20 units) = 12 minutes
1 batch of M (30 units) = 16 minutes
1 batch of B (40 units) = 20 minutesThis totals 48 minutes, leaving 72 minutes available.
After fulfilling minimum demand, we can produce more Cupcakes and Muffins:
Produce 5 batches of C (100 units) = 60 minutes
Then 1 batch of M (30 units) = 16 minutes
This totals 76 minutes, which exceeds the available 72 minutes.The best combination that fits within the 120 minutes while maximizing profit is:
80 B (2 batches) = 40 minutes
30 M (1 batch) = 16 minutes
100 C (5 batches) = 60 minutesTotal = 40 + 16 + 60 = 116 minutes.
Thus, the optimal production plan for Wednesday is A) 80 brownies, 30 muffins, and 100 cupcakes
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