Quidi Vidi Co. has 325 motors in its inventory at the start of the week. It will use all of these in its weekly production runs and then resupply its inventory for the next week. The carrying cost per
Motor is $84.26. The ﬁxed cost per order is $63. The variable cost per motor is $122.
How will the number of orders per year change if Quidi Vidi Co. adheres to the EOQ order level?

Question

Quizplus · Accepted Answer

First, we need to calculate the Economic Order Quantity (EOQ) with the given information:
EOQ = sqrt((2 * annual demand * fixed cost per order) / carrying cost per motor)

Annual demand = 325 motors/week * 52 weeks/year = 16,900 motors/year
EOQ = sqrt((2 * 16,900 * 63) / 84.26) = 236

This means that Quidi Vidi should order 236 motors each time it places an order to minimize its total inventory cost.

Next, we need to calculate the number of orders per year with the EOQ order level:
Number of orders per year = annual demand / EOQ = 16,900 / 236 = 71.61

However, since Quidi Vidi cannot order a fractional number of motors, it will need to round up to 72 orders per year.

Now, we need to calculate the number of orders per year without the EOQ order level to see how it changes:
Number of orders without EOQ = annual demand / order quantity
To determine the order quantity without EOQ, Quidi Vidi would need to look at various quantities and calculate the total cost of each to determine the most cost-effective option. However, since we are trying to determine how the number of orders per year will change if Quidi Vidi adheres to the EOQ order level, we can assume that without the EOQ, the order quantity will be different each time and not optimized for cost.

Therefore, since we do not have a specific order quantity without EOQ to use in the calculation, we can only look at the fixed cost per order to determine how the number of orders per year might change.

If the fixed cost per order is decreased, then Quidi Vidi would be incentivized to place more orders throughout the year since it would be less expensive to do so. However, since the fixed cost per order is not changing, the number of orders per year will only decrease if Quidi Vidi can increase the order quantity per order beyond the EOQ level.

To calculate how much the number of orders per year would change if Quidi Vidi increases the order quantity per order beyond the EOQ level, we can use the following formula:
New number of orders per year = annual demand / (EOQ + x)
where x is the number of additional motors per order beyond the EOQ level.

Plugging in the numbers, we get:
New number of orders per year = 16,900 / (236 + x)

We want to find the value of x that would result in a decrease of 72 orders per year from the EOQ level:
16,900 / (236 + x) = 72 more than 71.61
16,900 / (236 + x) = 143.61
(236 + x) = 117.22
x = 117.22 - 236 = -118.78

This negative value means that Quidi Vidi cannot increase the order quantity per order beyond the EOQ level and still have a total number of orders per year less than 72. Therefore, the answer is C) Increase of 107 orders, since the number of orders per year can only change by increasing or decreasing from the EOQ level, and it cannot decrease since the fixed cost per order is not changing.