Athens Co$.$ makes three products in a single facility. These products have the following unit product costs:

Product A Product B Product C

Direct material $$40\mathrm{.}00$ $$35\mathrm{.}00$ $$38\mathrm{.}00$

Direct labor $21\mathrm{.}0018\mathrm{.}5017\mathrm{.}50$

Variable manufacturing overhead $5\mathrm{.}507\mathrm{.}0011\mathrm{.}00$

Fixed manufacturing overhead $35\mathrm{.}0036\mathrm{.}0031\mathrm{.}00$

Unit cost $$101\mathrm{.}50$ $$96\mathrm{.}50$ $$97\mathrm{.}50$

Additional data concerning these products are listed below:

Product A Product B Product C

Mixing minutes per unit $5\mathrm{.}53\mathrm{.}55\mathrm{.}0$

Selling price per unit $$135\mathrm{.}00$ $$122\mathrm{.}00128\mathrm{.}00$

Variable selling cost per unit $$9\mathrm{.}50$ $$7\mathrm{.}00$ $$8\mathrm{.}75$

Monthly demand in units $2,4004,9004,200$

The mixing machines are potentially the constraint in the production facility. A total of $39,000$ minutes are available per month on these machines.

Direct labor is a variable cost in this company.

Required:

$$ How many minutes of mixing machine time would be required to satisfy demand for all three products?

$$ What is the contribution margin per minute individually for Products A$,$ B$,$ and C$?$