Assume that the price of silk ties in a perfectly competitive market

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Assume that the price of silk ties in a perfectly competitive market is $19 and that the typical
firm confronts the following costs:
Quantity
(ties per day) 0 1 2 3 4 5 6 7 8 9 10
Total cost $10 $17 $26 $37 $50 $65 $82 $101 $122 $145 $170
( a ) What is the profit-maximizing rate of output for the firm?
( b ) How much profit does the firm earn at that rate of output?
( c ) If the price of ties fell to $15, how many ties should the firm produce?
( d ) At what price should the firm shut down?