Question

Arah'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's optimal production schedule for organic liquid soap should be calculated by determining the least common multiple (LCM) of the production times based on demand, and then allocating production time accordingly to minimize switchovers and inventory.

Step-by-step explanation:

Arah's organic soap company is looking for an efficient production schedule for its four types of organic liquid soap—"regular", "lavender", "citrus", and "tea tree"—with demands of 150, 120, 75, and 50 kgs per hour respectively. The production process can output a combined 450 kgs per hour, but requires a 1.5-hour downtime to switch scents, during which no soap is produced. To meet the demand and minimize inventory, Sarah should calculate the least common multiple (LCM) of the production rates and schedule production in proportion to the demand.

To better understand the production needs, let's express the demand as a fraction of the production capability per hour (450 kgs):

• Regular: 150 kgs/450 kgs = 1/3 of production time
• Lavender: 120 kgs/450 kgs = 4/15 of production time
• Citrus: 75 kgs/450 kgs = 1/6 of production time
• Tea Tree: 50 kgs/450 kgs = 1/9 of production time

By determining the LCM of the production times and the fraction of production needed, Sarah can create a schedule that fulfills all demands with the fewest switchovers. This schedule should cycle in a way that the ratio of time spent on each soap is proportional to their respective demand.