A mixing machine $($Mixer$)$ needs the following operations:

$$ Loading$/$unloading Mixer: $6$ minutes

$$ Machine Mixing: $30$ minutes

$$ Cleaning the machine: $4$ minutes

$$ Travel to & Position for filling: $6$ minutes

Co $=$ $$12/$hr $($labor$)$

Cm $=$ $$25/$hr $($machine$)$

Please answer the following questions:

$1.$ Maximum number of mixers without creating idle time for mixers?

$2.$ How many mixers to minimize cost?

$3.$ If $2$ machines are assigned per operator, what will be the cost per unit?

$4.$ If the cost per machine is unknown, for what range of values Cm will the optimum

assignment remain the same?