Hello, Corky!
The AC Telephone Co. makes two styles of cordless telephones: Deluxe and Standard.
Each deluxe telephone nets the company $9 in profit, and each standard telephone nets $6.
Machines A and B are used to make both styles of telephones.
Each Deluxe telephone requries three hours on machine A and one hour on machine B.
Each Standard phone requires 2 hours on machine A and two hours on machine B.
An employee has an idea that frees 12 hours of machine A time and 8 hours of machine B time.
Determine the mix of telephones that can be made during this free time
that most effectively generates profit for the company within the given restraints.
This is a linear programming problem.
I'll assume you are familiar with the required knowldge.
Let $\displaystyle x$ = number of Deluxe phones to be made: .$\displaystyle x \geq 0$ [1]
Let $\displaystyle y$ = number of Standard phones to be made: .$\displaystyle y \geq 0$ [2]
The $\displaystyle x$ Deluxe phone take $\displaystyle 3x$ hours on machine A and $\displaystyle x$ hours on machine B.
The $\displaystyle y$ Standard phones take $\displaystyle 2y$ hours on machine A and $\displaystyle 2y$ hours on machine B.
Maximum time on machine A is 12 hours: .$\displaystyle 3x + 2y \:\leq\:12$ [3]
Maximum time on machine B is 8 hours: .$\displaystyle x + 2y \:\leq \:8$ [4]
Graph the region determined by [1], [2], [3] and [4]
. . and consider the vertices. Code:

6*
 *
 *
(0,4)o *
:::* *
:::::::* *
:::::::::::o (2,3)
:::::::::::::* *
:::::::::::::::* *
:::::::::::::::::* *
 +          o    *  
(0,0) (4,0) 8
We have the vertices: .$\displaystyle (0,0),\:(4,0),\;(2,3),\:(0,4)$
Test them in the profit function: .$\displaystyle P \:=\:9x + 6y$
. . and see which produces maximum profit.