Sarah\'s Organic Soap Company makes four kinds of organic liquid soap- \"regular

Question

Sarah's Organic Soap Company makes four kinds of organic liquid soap- "regular," "lavender, "citrus," and "tea tree." Demand for the four scents are 150, 100, 100, and 60 kgs per hour respectively. Sarah's production process can produce any soap at the rate of 475 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 (1) cycles repeatedly through the four scents, (2) meets the required demand and (3) minimizes the amount of inventory held. kgs How many kgs of "regular should Sarah produce before switching over to another scent?

Explanation / Answer

Assuming that sarah's production process produces all four scents one by one that is at first regular, then lavender, then citrus and then tea and then again regular and so on.

If in an hour sarah is producing regular soaps then after that hour it will require 1.5 hour to switch to produce lavender then 1 hour will be invest in producing lavender then again 1.5 hour require to switch then another 1 hour for citrus then another 1.5 hour to switch and then lastly 1 hour for tea tree and then agian 1.5 hour to switch and then only regular will be produced again.

hence from the 1st cycle of producing regular to next cycle of producing regular soaps it takes total of 1.5+1+1.5+1+1.5+1+1.5 = 9 hours.

In other words till sarah get another cycle of producing regular a gap of 9 hours existed and the demand for regular per hour is 150 kg thus demand of 9 hours will be 150*9 = 1350 soaps.

Thus at the first round of producing regular saop sarah should produce 1350 soaps to meet the demand of upcoming 9 hours till she can produce more of it.

Thus, 1350 kgs of regular soaps should be produced before switching to another soap. But as one hour can only produce 475kgs, sarah would require continous three hours to prdouce atleast 1350 kg to meet demand until next cycle.

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