Question

Sarah's Organic Soap Company makes four kinds of organic liquid soap: "regular," "lavender," "citrus," and "tea tree." Demands for the four scents are 150, 120, 75, and 50 kgs per hour, respectively. Sarah's production process can produce any soap at the rate of 450 kgs per hour, but 1.5 hours are needed to switch between scents. During those switchover times, the process doesn't produce any soap. Sarah's wants to choose a production schedule that (i) cycles repeatedly through the four scents, (ii) meets the required demand, and (iii) minimizes the amount of inventory held. (Round your answer to the nearest whole number.) a. Suppose Sarah's produces 12,000kgs of regular, 9600kgs of lavender, 6000kgs of citrus, and 4000 kgs of tea tree per batch. How much soap (kgs) can Sarah's produce per hour? kgs/hr (Round your answer to 1 decimal place.) b. Suppose Sarah's produces 12,000kgs of regular, 9600kgs of lavender, 6000kgs of citrus, and 4000kgs of tea tree per batch. What is the utilization (%) of the process? (Round your answer to the nearest whole number.) Suppose Sarah's produces 12,000kgs of regular, 9600kgs of lavender, 6000kgs of citrus, and c. 4000kgs of tea tree per batch. How much inventory (kgs) do they have on average of lavender kgs soap? (Round your answer to the nearest whole number.) d. How many kgs of "regular" should Sarah's produce before switching over to another scent? kgs

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Answer 1

The question concerns optimizing Sarah's Organic Soap Company's production schedule to meet demand for different scented soaps while minimizing inventory. It involves calculations for production rate, process utilization, average inventory, and production quantity before switching scents.

Step-by-step explanation:

The question relates to the operations management in Sarah's Organic Soap Company, requiring calculations based on the provided production data to establish an efficient production schedule.

Part a asks for the production rate per hour, which is calculated by summing up the total production for each soap scent and dividing by the total time taken, including production and switchover times. However, part b asks for the utilization rate, which is the total productive time divided by the total available time, expressed as a percentage. In part c, we calculate the average inventory held for lavender soap, which involves determining how long a batch lasts and how this translates to average inventory levels. Part d inquires about the quantity of "regular" soap to produce before switching scents, which would be based on demand and production rates to minimize inventory and downtime.

Specific mathematics for these individual parts are not provided as it requires additional data not included in the question, such as the length of the production cycle and the amount of time allowed for production of each scent.