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$?$

Using only the available $47,000$ minutes of machine time, how much of each product should be produced to maximize net operating income? $($Round down to the nearest whole units.$)$

Is there unmet demand for product$($s$)?$ If so$,$ how much and for which product$($s$)?$

Assume there is unmet product demand. How much in total should Athens Co$.$ be willing to pay for each additional hour of machine time?

Did variable selling cost per unit figure into any of your calculations? Which ones, if any?

Is there anything misleading about the figure given for fixed manufacturing overhead?

What is the significance of contribution margins with respect to determining how much of each product to produce to maximize company profits?

What is the significance of contribution margins with respect to determining how much Athens should pay for additional machine time?

Why isn$$t sales price or the difference between sales prices and the unit costs stated in the problem the best way of determining the priority Athens should follow in producing the products to maximize company profits?