Rosie's Company has three products, P$1,$ P$2,$ and P$3.$ The maximum Rosie's can sell is $82,000$ units of $P1,26,000$ units of P$2,$ and $14,000$ units of P$3.$ Rosie's has limited production capacity of $122,000$ machine hours. Machine hours per unit are as follows: P$1,1$ hour; P$2,2$ hours; P$3,4$ hours. Contribution margin per unit is $$5$ for $P1,$$$15$ for P $2,$ and $$25$ for P $3.$ What is the most profitable sales mix for Rosie's Company?

Multiple Choice

$12,600$ P$1,27,000$ P$2,12,600$ P$3.$

$14,000$ P$1,26,000$ P$2,14,000$ P$3.$

$12,600$ P$1,26,000$ P$2,14,000$ P$3.$

$14,000$ P$1,24,000$ P$2,14,000$ P$3.$

$18,200$ P$1,24,000$ P$2,14,000$ P$3.$