Question

arah’s Organic Soap Company makes four kinds of organic liquid soap- “regular”, “lavender”, “citrus” and “tea tree”. 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.

Suppose Sarah would like to operate at exactly ¾ of process capacity. How many kilograms of citrus does she needs to produce before switching over to another scent? Assume Sarah would like to meet the original demand proportions of scents.

a.3076 kilograms

b. 2461
c. 1538
d. 1025
e. 250

Answer 1

Total demand rate = 150+120+75+50 = 395 kg per hour

Production rate = 450 kg per hour

Let Q be the desired batch size (of all 4 flavors clueless.

For Q batch size, production cycte time = Q/450+1.5*4

Demand cycle time = Q/395

For 3/4 of process capacity, Q/395 = .75*(Q/450+6)

=> Q/395-Q/600 = 4.5

=> Q = 5202 kg (of all four flavors combined)

Kilograms of Citrus to be produced before switching over to another scent = 5202*75/395 = 988 Kilograms