Question

The maintenance department of a large hospital uses about 816 cases of liquid cleanser annually. Ordering costs are $12 and carrying costs are $4 per case. The new price schedule is as follows: Quantity Unit Cost 1-49 $20 ' 50-79 $18 ~ 80-99 $17 .3 100 or more $16 Determine the optimal order quantity and the total cost.

Answer 1

The optimal order quantity is 98 cases of liquid cleanser and the total cost is estimated to be $295.96.

Step-by-step explanation:

To determine the optimal order quantity and total cost, we can use the Economic Order Quantity (EOQ) formula. The EOQ formula is given by:

EOQ = sqrt((2 × D × S) / H)

Where:

• D = Demand (number of cases) = 816
• S = Ordering cost per order = $12
• H = Carrying cost per unit per year = $4

Let's substitute the given values into the formula:

EOQ = sqrt((2 × 816 × 12) / 4) = sqrt(9792) = 98.95

Therefore, the optimal order quantity is 98 cases. To find the total cost, we can use the Total Cost formula:

Total Cost = (D / EOQ) × S + (EOQ / 2) × H

Substituting the values, we get:

Total Cost = (816 / 98) × 12 + (98 / 2) × 4 = 8.33 × 12 + 49 × 4 = 99.96 + 196 = $295.96

Therefore, the estimated total cost for ordering 98 cases of liquid cleanser is $295.96.

Answer 2

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Step-by-step explanation: