Electro Company manufactures transmissions for electric cars. Management reports ending finished goods inventory for the first quarter at $196,800$ units. The following unit sales are budgeted during the rest of the year: second quarter, $492,000$ units; third quarter, $415,000$ units; and fourth quarter, $311,500$ units. Company policy calls for the ending finished goods inventory of a quarter to equal $40\%$ of the next quarter's budgeted unit sales.

Prepare a production budget for both the second and third quarters that shows the number of transmissions to manufacture.