Beauty Bar Soap is produced on a production line that has an annual capacity of 79,126 cases (310 business days per year). The annual demand is estimated at 21,764 cases, with the demand rate essentially constant throughout the year. The cleaning, preparation, and setup of the production line cost approximately $155. The manufacturing cost per case is $5.1, and the annual carrying cost is figured at 23% of the manufacturing cost per case. What is the maximum level of inventory at the optimal production lot size with the minimum inventory cost?

The maximum level of inventory at the optimal production lot size with the minimum inventory cost is 2,041 units

Explanation:

According to the given data we have the following:

Annual Demand D = 21,764

Production Capacity P = 79,126

Set up Cost S = $155

Manufacturing Coast = $5.1

Carrying Cost H = $5.1*23% = 1.173

To calculate maximum level of inventory at the optimal production lot size with the minimum inventory cost first we need to calculate the EPQ as follows:

EPQ = (2DS/(H*(1-(D/P^(1/2)

EPQ = (2*21,764*155/(1.173*(1-(21,764/79,126^(1/2)

EPQ=(6,746,840/0.8503605136))^(1/2)

EPQ=2,816 Units

Therefore, in order to calculate the he maximum level of inventory at the optimal production lot size with the minimum inventory cost we would have to use the following formula:

Imax = EOQ*(1-(D/P))

Imax = 2,816*(1-(21,764/79,126))

Imax=2,041 units

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