Birch Company normally produces and sells $46,000$ units of RG$-6$ each month. The selling price is $$30$ per unit, variable costs are $$10$ per unit, fixed manufacturing overhead costs total $$195,000$ per month, and fixed selling costs total $$38,000$ per month.

Employment$-$contract strikes in the companies that purchase the bulk of the RG$-6$ units have caused Birch Company$$s sales to temporarily drop to only $9,000$ units per month. Birch Company estimates that the strikes will last for two months, after which time sales of RG$-6$ should return to normal. Due to the current low level of sales, Birch Company is thinking about closing down its own plant during the strike, which would reduce its fixed manufacturing overhead costs by $$46,000$ per month and its fixed selling costs by $10\%.$ Start$-$up costs at the end of the shutdown period would total $$16,000.$ Because Birch Company uses Lean Production methods, no inventories are on hand.

Required:

$1.$ What is the financial advantage $($disadvantage$)$ if Birch closes its own plant for two months?

$2.$ Should Birch close the plant for two months?

$3.$ At what level of unit sales for the two$-$month period would Birch Company be indifferent between closing the plant or keeping it open?