Samuelson has a beginning inventory balance on january 1 of 12,000 units and desires an ending balance of 20% of the next month’s sales. if sales are expected to be 17,000 for january and 20,000 for february, what amount of units does samuelson have to produce during the month of january?

Samuelson has to produce 9,000 units in January

Explanation:

First, the statement that Samuelson's ending balance is 20% of the next month' sales means that, after all the sales that month, the amount of units left over should be 20% of the forecast sale for the next month.

Since we are calculating for the month of January, the ending unit of January should be 20% of the unit for February. This 20% is calculated as follows:

unit expected to be sold in February = 20,000

20% of 20,000 = 20/100 × 20000 = 0.2 × 20000 = 4000 units.

So at the end of January's sales, we should have 4,000 units left in the inventory.

Next, were are given that the expected sale unit in January is 17,000 units, also, remember that in January, there was a starting inventory of 12,000 units.

Since sale is expected to be 17,000, and we know that we need to produce 4,000 units of excess to end the month, plus the 12,000 units already available, to calculate the number of units to be produced outside the excess (that will completely satisfy sales);

we subtract 12,000 from 17,000; which is 17,000 - 12,000 = 5000.

Therefore to exactly meet up the expected sales, Samuelson needs to produce 5000 more units but remember that he also wishes to end the month with 20% of the next month's sale which is 4000 units.

Therefore, total amount to be produced in January = 5000 + 4000 = 9,000 units