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 = number of Deluxe phones to be made: . [1]
Let = number of Standard phones to be made: . [2]
The Deluxe phone take hours on machine A and hours on machine B.
The Standard phones take hours on machine A and hours on machine B.
Maximum time on machine A is 12 hours: . [3]
Maximum time on machine B is 8 hours: . [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: .
Test them in the profit function: .
. . and see which produces maximum profit.