# algebra help

• Jun 20th 2007, 09:56 AM
lizard4
algebra help
a small firm produces both am and am/fm car radios. the am radios take 15h to produce and the am/fm radios take 20h..the number of production hours is limited to 300h per week. The plant's capacity is limited to a total of 18 radios per week, and existing orders require that at least 4 am radios and at least 3am/fm radios be produced per week. write a system of inequalities representing this situation. Then draw a graph of the feasible region given this condition in which x is the number of am radios and y is the number of am/fm radios
• Jun 20th 2007, 10:39 AM
earboth
Quote:

Originally Posted by lizard4
a small firm produces both am and am/fm car radios. the am radios take 15h to produce and the am/fm radios take 20h..the number of production hours is limited to 300h per week. The plant's capacity is limited to a total of 18 radios per week, and existing orders require that at least 4 am radios and at least 3am/fm radios be produced per week. write a system of inequalities representing this situation. Then draw a graph of the feasible region given this condition in which x is the number of am radios and y is the number of am/fm radios

Hello,

let x be the amount of am radios;
let y be the amount of am/fm radios

Then you get the following system of inequaltities:

$x+y\leq 18 \Longrightarrow y \leq -x+18$
$x\geq 4$
$y \geq 3$
$15x + 20y \leq 300 \Longrightarrow y \leq -\frac{3}{4}x + 15$

I've attached a diagram of the graph