Sandstone Corporation has one of its manufacturing plants operating on a single shift five-day week. The plant is operation at its full capacity (24,000 units of output per week) without the use of overtime or extra shifts. Fixed costs for single-shift operation amount to $90,000 per week. The average variable cost is a constant $30 per unit, at all output rates, up to 24,000 units per week. The company has received an order to produce an extra 4,000 units per week beyond the current single-shift maximum capacity. Two options are being considered to fill the new order:

Option 1. Increase the plant’s output to 36,000 units a week by adding overtime, by adding Saturday operations, or both. No increase in fixed cost is entailed, but the variable cost is $36 per unit for any output in excess or 24,000 units per week, up to the 36,000 unit capacity.

Option 2. Operate a second shift. The maximum capacity of the second shift is 21,000 units per week. The variable cost of the second shift is $31.50 per unit, and the operation of the second shift entails additional fixed cost of $13,500 per week.

a) Determine the range of operating volume that will make Option 1 profitable.

b) Determine the range of operating volume that will make Option 2 profitable.