# Help! This is confusing!

• Jan 22nd 2007, 04:38 PM
Corky5
Help! This is confusing!
The AC Telephone Company manufactures 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 of machine A time and one hour of machine B time. An employee has an idea that frees twelve hours of machine A time and eight 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. :eek: :eek: :eek:

Plese Help! It is really hard and confusing@
• Jan 22nd 2007, 07:48 PM
Soroban
Hello, Corky5!

It's confusing to me, too . . . You left out part of the problem.

Each standard telephone requires __ hours on machine A and __ hours on machine B.

• Jan 25th 2007, 01:54 PM
Corky5
Sry... here is the part i left out-Each standard telephone requires two hours of machine A time and two hours of machine B time....Thx
• Jan 25th 2007, 04:16 PM
Soroban
Hello, Corky!

Quote:

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.