Question

Rossini Company has budgeted production for next year as follows:

Quarter	First	Second	Third	Fourth
Units to be sold	53,400	80,200	94,000	?

At the beginning of the year, Rossini is expected have 5,340 units of the product. At the end of each quarter, Rossini would like to have an inventory equal to 10% of the sales units of the next quarter.

How many units should Rossini produce in the second quarter?

A. 80,200 units
B. 81,580 units
C. 56,080 units
D. 78,820 units

E. None of the above

Answer 1

Number of units Rossini should produce in the second quarter: B. 81,580 units

• At the end of each quarter, Rossini would like to have an inventory equal to 10% of the sales units of the next quarter.
• Therefore, inventory at the end of each quarter are: (TABLE 1)

• Quarter		First	Second
  Sales units for NEXT quarter	A	80,200	94,000
  Inventory at the end of the quarter	A × 10%	8,020	9,400

• Note that 2^nd row in the above table shows sales units for next quarter. For instance, 80,200 are sales units for the second quarter. Closing inventory for each quarter is 10% of 'A' above as specified in the question.
• It is given that at the beginning of the year, Rossini is expected to have 5,340 units of the product. i.e. Inventory at the beginning of Quarter 1 = 5,340 units.
• Now, production units for the first and second quarters are as follows:

• Quarter	First	Second
  Beginning inventory	5,340	8,020
  Add: produced units (to be found)	56,080	81,580
  Less: sold units	53,400	80,200
  Closing inventory (table 1)	8,020	9,400

• We know that closing inventory is found by the following equation:

Closing inventory = Opening inventory + produced units - sold units

• In this question, we need to find the number of units to be produced. Therefore, rearranging the above equation:

Produced units = Closing inventory - opening inventory + sold units

• Units produced during the first quarter = 8,020 - 5,340 + 53,400 = 56,080 units
• Units produced during the second quarter = 9,400 - 8,020 + 80,200 = 81,580 units