2. Punkey Electronics, a small manufacturer of electronic research equipment, has approximately 7,000 items in its inventory. They just hired Joe Detail to manage the inventory. Joe has determined that 10% of the items in inventory are A items, 35% are B items and 55% are C items. He would like to set up a system where all the A items are counted monthly (every month has 20 working days), B items are counted quarterly (every 60 working days), and all C items are counted semiannually (every 120 working days). How many items of each classification and in total need to be counted each day?
To determine how many items of each classification and in total need to be counted each day, we need to calculate the counts based on the given percentages and counting schedules.
Let's start by calculating the number of A, B, and C items separately:
1. A items:
The inventory has approximately 7,000 items, and 10% of them are classified as A items.
Number of A items = 10% of 7,000 = 0.10 * 7,000 = 700 items
2. B items:
The inventory has approximately 7,000 items, and 35% of them are classified as B items.
Number of B items = 35% of 7,000 = 0.35 * 7,000 = 2,450 items
3. C items:
The inventory has approximately 7,000 items, and 55% of them are classified as C items.
Number of C items = 55% of 7,000 = 0.55 * 7,000 = 3,850 items
Now, let's calculate the counting frequency for each type of item:
1. A items: counted monthly (every 20 working days).
Number of A items counted per day = Number of A items / counting period
Number of A items counted per day = 700 items / 20 days = 35 items per day
2. B items: counted quarterly (every 60 working days).
Number of B items counted per day = Number of B items / counting period
Number of B items counted per day = 2,450 items / 60 days = 40.83 items per day (rounded to 41 items per day)
3. C items: counted semiannually (every 120 working days).
Number of C items counted per day = Number of C items / counting period
Number of C items counted per day = 3,850 items / 120 days = 32.08 items per day (rounded to 32 items per day)
To find the total number of items counted each day, we sum the counts for each type of item:
Total items counted per day = Number of A items counted per day + Number of B items counted per day + Number of C items counted per day
Total items counted per day = 35 items per day + 41 items per day + 32 items per day
Total items counted per day = 108 items per day
Therefore, a total of 108 items need to be counted each day, including 35 A items, 41 B items, and 32 C items.
To determine how many items of each classification and in total need to be counted each day, we need to calculate the count frequency for each item category.
Step 1: Calculate the count frequency for A items:
Since A items are counted monthly, the count frequency for A items would be 1/20 (one count every 20 working days).
Number of A items = 10% of 7,000 = 0.10 * 7,000 = 700
A item count frequency per day = (Number of A items) / (working days per count)
= 700 / 20
= 35 items per day
Step 2: Calculate the count frequency for B items:
B items are counted quarterly, which means the count frequency for B items would be 1/60 (one count every 60 working days).
Number of B items = 35% of 7,000 = 0.35 * 7,000 = 2,450
B item count frequency per day = (Number of B items) / (working days per count)
= 2,450 / 60
= 40.83 items per day
Since we cannot count a fraction of an item, we need to round up the count frequency for B items to the nearest whole number.
Rounding up, B item count frequency per day = 41 items per day
Step 3: Calculate the count frequency for C items:
C items are counted semiannually, so the count frequency for C items would be 1/120 (one count every 120 working days).
Number of C items = 55% of 7,000 = 0.55 * 7,000 = 3,850
C item count frequency per day = (Number of C items) / (working days per count)
= 3,850 / 120
= 32.083 items per day
Again, rounding up to the nearest whole number, C item count frequency per day = 33 items per day
Step 4: Calculate the total number of items counted each day:
Total items counted per day = Number of A items per day + Number of B items per day + Number of C items per day
= 35 items per day + 41 items per day + 33 items per day
= 109 items per day
So, a total of 109 items need to be counted each day, consisting of 35 A items, 41 B items, and 33 C items.