Question

Sarah's organic soap company makes four kinds of organic liquid soap- "regular", "lavender", "citrus" and "tea tree". The demand 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 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. What is the production schedule that Sarah should choose?

Answer 1

Sarah should allocate production time to each soap scent based on the demand ratios within the 18 hours of actual production time available per cycle, accounting for the 6 hours of switchover time, to meet demand precisely with minimal inventory.

Step-by-step explanation:

The student is asking for the optimal production schedule that Sarah's organic soap company should choose to meet demand, avoid excess inventory, and account for the changeover times between different soap scents. To solve this, we must determine how long each scent should be produced within each cycle to meet demand without overproducing.

We start by calculating the total production time available per cycle, subtracting the time needed for switchovers. With 1.5 hours needed to switch between each of the four scents, the total switchover time is 1.5 hours * 4 = 6 hours. In a continuous 24-hour production cycle, this leaves us with 18 hours actually available for soap production.

The demand ratio for 'regular', 'lavender', 'citrus', and 'tea tree' scents is 150:120:75:50. To meet the demand proportionately, we can allocate production time based on these ratios out of the 18 hours available. We find the common denominator for the ratios and allocate production time according to these proportions:

• 'Regular': 9 hours
• 'Lavender': 7.2 hours
• 'Citrus': 4.5 hours
• 'Tea Tree': 3 hours

By producing each soap for the allocated time, Sarah will meet the hourly demand exactly, without overproducing and with minimal inventory held.