Bailey Products produces two joint products $($A and B$).$ Prior to the split$-$off point, the company incurs costs of $$6,000.$ Product A weighs $30$ pounds, and Product B weighs $120$ pounds. Product A sells for $$100$ per pound, and Product B sells for $$35$ per pound.

$1.$ Based on a physical measure of output, allocate joint costs to Products A and B

$2.$ Compare the costs to the selling prices. Should the company sell products whose selling price is$$less than the allocated joint cost?