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Calculate the numerical value of the quantity asked.For a carpet manufacturer, the estimated annual demand is 20,000 yards of carpet with an annual carrying cost of $2.75 per yard. The manufacturing facility operates for 360 days and produces 400 yards of carpet per day. The cost of setting up the manufacturing process is $720. Determine the optimal order size. (answer should be correct to one decimal place)

Question

Calculate the numerical value of the quantity asked.For a carpet manufacturer, the estimated annual demand is 20,000 yards of carpet with an annual carrying cost of 2.75peryard.Themanufacturingfacilityoperatesfor360daysandproduces400yardsofcarpetperday.Thecostofsettingupthemanufacturingprocessis2.75 per yard. The manufacturing facility operates for 360 days and produces 400 yards of carpet per day. The cost of setting up the manufacturing process is 720. Determine the optimal order size. (answer should be correct to one decimal place)

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Solution

To calculate the optimal order size, we can use the Economic Order Quantity (EOQ) model. The formula for EOQ is:

EOQ = sqrt((2DS)/H)

where: D = Demand rate per year S = Setup or ordering cost per order H = Holding or carrying cost per unit per year

Given: D = 20,000 yards S = 720H=720 H = 2.75 per yard

Substituting these values into the formula, we get:

EOQ = sqrt((220000720)/2.75)

Now, calculate the value inside the square root:

= sqrt((28800000)/2.75)

= sqrt(10472727.27)

Finally, take the square root:

EOQ = 3236.8 yards

So, the optimal order size is approximately 3236.8 yards.

This problem has been solved

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