Tally Inc. makes four products in a single facility. Data concerning these products appear below:

$$

$$

Products

$$

$$

A

B

C

D

$$

Selling price per unit

$

$42\mathrm{.}30$

$

$50\mathrm{.}00$

$

$37\mathrm{.}60$

$

$33\mathrm{.}50$

Variable cost per unit

$

$23\mathrm{.}50$

$

$32\mathrm{.}80$

$

$22\mathrm{.}00$

$

$22\mathrm{.}30$

Milling machine minutes per unit

$$

$3\mathrm{.}00$

$$

$2\mathrm{.}00$

$$

$2\mathrm{.}60$

$$

$1\mathrm{.}50$

Monthly demand in units

$$

$1,000$

$$

$8,000$

$$

$3,000$

$$

$3,000$

Milling machines are potentially the constraint in the production facility. A total of $29,200$ minutes are available per month on these machines.$$

$(1).$ How many minutes of milling machine time would be required to satisfy demand for all four products?$(4$ points$)$

$(2).$ Which product makes the MOST profitable use of the milling machines?$(3$ points$)$

$(3).$ A total of $29,200$ minutes is available per month on these machines. What plan would maximize profits?$(4$ points$)$

$(4).$ Up to how much should the company be willing to pay for one additional minute of milling machine time if the company has made the best use of the existing milling machine capacity? $(4$ points$)$