Levy produces three types of denim jeans: black, blue, and red. The company has a color dyeing machine that is currently being used at $100\%$ of its capacity. All other machines have excess capacity. The color dyeing machine has a maximum capacity of $15,000$ minutes per month. Data concerning the three types of jeans appear below.

Product

Black

Blue

Red

Selling price per unit

$$50$

$$50$

$$60$

Variable expenses per unit

$30$

$22$

$28$

Monthly demand $($# of units$)$

$8,000$

$8,000$

$8,000$

Machine time required

$1$ minute

$1\mathrm{.}25$ minutes

$2$ minutes

Now a third party offers to rent another dyeing machine $($exactly the same as the one Levy currently has$)$ to Levy at the price of $$18$ per minute. The rental term states that Levy can rent the machine for up to $15,000$ minutes a month $($Levy pays $$18$ times the number of minutes it uses the machine$).$

How many minutes per month should Levy rent the dyeing machine for from the third party?