Question 87272
Since the total production hours are limited to 300 hours, this inequality would apply:


{{{15x+20y<300}}} 


The idea of this inequality is if we plug in values for x and y, we must stay under 300 (since its limited to 300 hrs a week)


For instance, lets say we produced 2 AM radios and 4 AM/FM radios, we could find out if we met the restrictions by plugging them in like this


{{{15(2)+20(4)<300}}} ->{{{30+80<300}}}->{{{110<300}}}

So to produce these units, we stay within 300 hrs



Also, since the total number of radios produced is limited to 18, this means this inequality would apply:


{{{x+y<18}}} basically the sum of all that is produced must be less than 18 units


Also, since you cannot produce negative units, it makes sense to restrict x and y to positive numbers only. So these inequalities would do just that:


{{{x>=0}}} Inequality for positive x values
{{{x>=0}}} Inequality for positive y values


So basically we need to graph this system of inequalities:


{{{15x+20y<300}}}

{{{x+y<18}}}

{{{x>=0}}}

{{{y>=0}}}




So now lets graph this system of inequalities:



Start with the given system of inequalities

{{{15x+20y<300}}}

{{{x+y<18}}}

{{{x>=0}}}

{{{y>=0}}}


In order to graph this system of inequalities, we need to graph each inequality one at a time.



First lets graph the first inequality {{{15x+20y<300}}}

In order to graph {{{15x+20y<300}}}, we need to graph the <b>equation</b> {{{15x+20y=300}}} (just replace the inequality sign with an equal sign).
So lets graph the line {{{15x+20y=300}}} (note: if you need help with graphing, check out this <a href=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver<a>)


{{{ graph( 500, 500, -20, 20, -20, 20, -(3/4)x+15) }}} graph of {{{15x+20y=300}}} 

Now lets pick a test point, say (0,0) (any point will work, but this point is the easiest to work with), and evaluate the inequality {{{15x+20y<300}}}


Substitute (0,0) into the inequality

{{{15(0)+20(0)<300}}} Plug in {{{x=0}}} and {{{y=0}}}

{{{0<300}}} Simplify

Since this inequality is true, we simply shade the entire region that contains (0,0) (note: even though the shaded region looks like it's a fixed size, it is a region with an area of infinite size. The reason it looks like it stops is due to the graphing limitations of this site. But in reality, the shaded region occupies the whole area on one side of the red line.) 

{{{drawing( 500, 500, -20, 20, -20, 20,
graph(  500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-1),
graph(  500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-2),
graph(  500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-3),
graph(  500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-4),
graph(  500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-5),
graph(  500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-6),
graph(  500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-7),
graph(  500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-8),
graph(  500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-9),
graph(  500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-10),
graph(  500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-11),
graph(  500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-12),
graph(  500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-13),
graph(  500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-14),
graph(  500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-15),
graph(  500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-16),
graph(  500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-17),
graph(  500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-18),
graph(  500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-19))}}} Graph of {{{15x+20y<300}}} with the boundary (which is the line {{{15x+20y=300}}} in red) and the shaded region (in green) 
(note: since the inequality contains a less-than sign, this means the boundary is excluded. This means the solid line is really a dashed line)

---------------------------------------------------------------



Now lets graph the second inequality {{{x+y<18}}}

In order to graph {{{x+y<18}}}, we need to graph the <b>equation</b> {{{x+y=18}}} (just replace the inequality sign with an equal sign).
So lets graph the line {{{x+y=18}}} (note: if you need help with graphing, check out this <a href=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver<a>)


{{{ graph( 500, 500, -20, 20, -20, 20, -x+18) }}} graph of {{{x+y=18}}} 

Now lets pick a test point, say (0,0) (any point will work, but this point is the easiest to work with), and evaluate the inequality {{{x+y<18}}}


Substitute (0,0) into the inequality

{{{(0)+(0)<18}}} Plug in {{{x=0}}} and {{{y=0}}}

{{{0<18}}} Simplify

Since this inequality is true, we simply shade the entire region that contains (0,0)

{{{drawing( 500, 500, -20, 20, -20, 20,
graph(  500, 500, -20, 20, -20, 20,-x+18,-x+18+-1),
graph(  500, 500, -20, 20, -20, 20,-x+18,-x+18+-2),
graph(  500, 500, -20, 20, -20, 20,-x+18,-x+18+-3),
graph(  500, 500, -20, 20, -20, 20,-x+18,-x+18+-4),
graph(  500, 500, -20, 20, -20, 20,-x+18,-x+18+-5),
graph(  500, 500, -20, 20, -20, 20,-x+18,-x+18+-6),
graph(  500, 500, -20, 20, -20, 20,-x+18,-x+18+-7),
graph(  500, 500, -20, 20, -20, 20,-x+18,-x+18+-8),
graph(  500, 500, -20, 20, -20, 20,-x+18,-x+18+-9),
graph(  500, 500, -20, 20, -20, 20,-x+18,-x+18+-10),
graph(  500, 500, -20, 20, -20, 20,-x+18,-x+18+-11),
graph(  500, 500, -20, 20, -20, 20,-x+18,-x+18+-12),
graph(  500, 500, -20, 20, -20, 20,-x+18,-x+18+-13),
graph(  500, 500, -20, 20, -20, 20,-x+18,-x+18+-14),
graph(  500, 500, -20, 20, -20, 20,-x+18,-x+18+-15),
graph(  500, 500, -20, 20, -20, 20,-x+18,-x+18+-16),
graph(  500, 500, -20, 20, -20, 20,-x+18,-x+18+-17),
graph(  500, 500, -20, 20, -20, 20,-x+18,-x+18+-18),
graph(  500, 500, -20, 20, -20, 20,-x+18,-x+18+-19))}}} Graph of {{{x+y<18}}} with the boundary (which is the line {{{x+y=18}}} in red) and the shaded region (in green) 
(note: since the inequality contains a less-than sign, this means the boundary is excluded. This means the solid line is really a dashed line)

---------------------------------------------------------------



Now lets graph the third inequality {{{x>=0}}}

In order to graph {{{x>=0}}}, we need to graph the <b>equation</b> {{{x=0}}} (just replace the inequality sign with an equal sign).
So lets graph the line {{{x=0}}} (note: if you need help with graphing, check out this <a href=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver<a>)


{{{ graph( 500, 500, -20, 20, -20, 20, 1000(x-0)) }}} graph of {{{x=0}}} (note:the graph is the line that is overlapping the y-axis. So it may be hard to see)

Now lets pick a test point, say (0,0) (any point will work, but this point is the easiest to work with), and evaluate the inequality {{{x>=0}}}


Substitute (0,0) into the inequality

{{{(0)>=0}}} Plug in {{{x=0}}} and {{{y=0}}}

{{{0>=0}}} Simplify

Since this inequality is true, we simply shade the entire region that contains (0,0)

{{{drawing( 500, 500, -20, 20, -20, 20,
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-1)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-2)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-3)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-4)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-5)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-6)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-7)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-8)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-9)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-10)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-11)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-12)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-13)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-14)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-15)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-16)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-17)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-18)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-19)))}}} Graph of {{{x>=0}}} with the boundary (which is the line {{{x=0}}} in red) and the shaded region (in green) 
(note: since the inequality contains a less-than sign, this means the boundary is excluded. This means the solid line is really a dashed line)

---------------------------------------------------------------



Now lets graph the fourth inequality {{{y>=0}}}

In order to graph {{{y>=0}}}, we need to graph the <b>equation</b> {{{y=0}}} (just replace the inequality sign with an equal sign).
So lets graph the line {{{y=0}}} (note: if you need help with graphing, check out this <a href=http://www.algebra.com/algebra/homework/Linear-equations/graphing-linear-equations.solver>solver<a>)


{{{ graph( 500, 500, -20, 20, -20, 20, 0) }}} graph of {{{y=0}}} (note:the graph is the line that is overlapping the x-axis. So it may be hard to see)

Now lets pick a test point, say (0,0) (any point will work, but this point is the easiest to work with), and evaluate the inequality {{{y>=0}}}


Substitute (0,0) into the inequality

{{{(0)>=0}}} Plug in {{{x=0}}} and {{{y=0}}}

{{{0>=0}}} Simplify

Since this inequality is true, we simply shade the entire region that contains (0,0)

{{{drawing( 500, 500, -20, 20, -20, 20,
graph(  500, 500, -20, 20, -20, 20,0,0+1),
graph(  500, 500, -20, 20, -20, 20,0,0+2),
graph(  500, 500, -20, 20, -20, 20,0,0+3),
graph(  500, 500, -20, 20, -20, 20,0,0+4),
graph(  500, 500, -20, 20, -20, 20,0,0+5),
graph(  500, 500, -20, 20, -20, 20,0,0+6),
graph(  500, 500, -20, 20, -20, 20,0,0+7),
graph(  500, 500, -20, 20, -20, 20,0,0+8),
graph(  500, 500, -20, 20, -20, 20,0,0+9),
graph(  500, 500, -20, 20, -20, 20,0,0+10),
graph(  500, 500, -20, 20, -20, 20,0,0+11),
graph(  500, 500, -20, 20, -20, 20,0,0+12),
graph(  500, 500, -20, 20, -20, 20,0,0+13),
graph(  500, 500, -20, 20, -20, 20,0,0+14),
graph(  500, 500, -20, 20, -20, 20,0,0+15),
graph(  500, 500, -20, 20, -20, 20,0,0+16),
graph(  500, 500, -20, 20, -20, 20,0,0+17),
graph(  500, 500, -20, 20, -20, 20,0,0+18),
graph(  500, 500, -20, 20, -20, 20,0,0+19))}}} Graph of {{{y>=0}}} with the boundary (which is the line {{{y=0}}} in red) and the shaded region (in green) 
(note: since the inequality contains a less-than sign, this means the boundary is excluded. This means the solid line is really a dashed line)

---------------------------------------------------------------



So we essentially have these 4 regions:


Region #1
{{{drawing( 500, 500, -20, 20, -20, 20,
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-1),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-2),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-3),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-4),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-5),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-6),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-7),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-8),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-9),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-10),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-11),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-12),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-13),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-14),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-15),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-16),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-17),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-18),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-19))}}} Graph of {{{15x+20y<300}}}



Region #2
{{{drawing( 500, 500, -20, 20, -20, 20,
graph( 500, 500, -20, 20, -20, 20,-x+18),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-1),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-2),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-3),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-4),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-5),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-6),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-7),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-8),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-9),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-10),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-11),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-12),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-13),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-14),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-15),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-16),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-17),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-18),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-19))}}} Graph of {{{x+y<18}}}



Region #3
{{{drawing( 500, 500, -20, 20, -20, 20,
graph( 500, 500, -20, 20, -20, 20,1000(x-0)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-1)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-2)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-3)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-4)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-5)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-6)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-7)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-8)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-9)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-10)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-11)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-12)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-13)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-14)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-15)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-16)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-17)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-18)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-19)))}}} Graph of {{{x>=0}}}



Region #4
{{{drawing( 500, 500, -20, 20, -20, 20,
graph( 500, 500, -20, 20, -20, 20,0),
graph( 500, 500, -20, 20, -20, 20,0,0+1),
graph( 500, 500, -20, 20, -20, 20,0,0+2),
graph( 500, 500, -20, 20, -20, 20,0,0+3),
graph( 500, 500, -20, 20, -20, 20,0,0+4),
graph( 500, 500, -20, 20, -20, 20,0,0+5),
graph( 500, 500, -20, 20, -20, 20,0,0+6),
graph( 500, 500, -20, 20, -20, 20,0,0+7),
graph( 500, 500, -20, 20, -20, 20,0,0+8),
graph( 500, 500, -20, 20, -20, 20,0,0+9),
graph( 500, 500, -20, 20, -20, 20,0,0+10),
graph( 500, 500, -20, 20, -20, 20,0,0+11),
graph( 500, 500, -20, 20, -20, 20,0,0+12),
graph( 500, 500, -20, 20, -20, 20,0,0+13),
graph( 500, 500, -20, 20, -20, 20,0,0+14),
graph( 500, 500, -20, 20, -20, 20,0,0+15),
graph( 500, 500, -20, 20, -20, 20,0,0+16),
graph( 500, 500, -20, 20, -20, 20,0,0+17),
graph( 500, 500, -20, 20, -20, 20,0,0+18),
graph( 500, 500, -20, 20, -20, 20,0,0+19))}}} Graph of {{{y>=0}}}





When these inequalities are graphed on the same coordinate system, the regions overlap to produce this region. It's a little hard to see, but after evenly shading each region, the intersecting region will be the most shaded in.




{{{drawing( 500, 500, -20, 20, -20, 20,
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-1),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-2),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-3),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-4),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-5),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-6),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-7),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-8),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-9),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-10),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-11),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-12),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-13),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-14),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-15),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-16),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-17),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-18),
graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-(3/4)x+15+-19),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-1),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-2),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-3),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-4),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-5),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-6),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-7),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-8),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-9),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-10),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-11),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-12),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-13),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-14),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-15),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-16),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-17),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-18),
graph( 500, 500, -20, 20, -20, 20,-x+18,-x+18+-19),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-1)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-2)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-3)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-4)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-5)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-6)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-7)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-8)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-9)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-10)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-11)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-12)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-13)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-14)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-15)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-16)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-17)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-18)),
graph( 500, 500, -20, 20, -20, 20,1000(x-0),1000(x-0+-19)),
graph( 500, 500, -20, 20, -20, 20,0,0+1),
graph( 500, 500, -20, 20, -20, 20,0,0+2),
graph( 500, 500, -20, 20, -20, 20,0,0+3),
graph( 500, 500, -20, 20, -20, 20,0,0+4),
graph( 500, 500, -20, 20, -20, 20,0,0+5),
graph( 500, 500, -20, 20, -20, 20,0,0+6),
graph( 500, 500, -20, 20, -20, 20,0,0+7),
graph( 500, 500, -20, 20, -20, 20,0,0+8),
graph( 500, 500, -20, 20, -20, 20,0,0+9),
graph( 500, 500, -20, 20, -20, 20,0,0+10),
graph( 500, 500, -20, 20, -20, 20,0,0+11),
graph( 500, 500, -20, 20, -20, 20,0,0+12),
graph( 500, 500, -20, 20, -20, 20,0,0+13),
graph( 500, 500, -20, 20, -20, 20,0,0+14),
graph( 500, 500, -20, 20, -20, 20,0,0+15),
graph( 500, 500, -20, 20, -20, 20,0,0+16),
graph( 500, 500, -20, 20, -20, 20,0,0+17),
graph( 500, 500, -20, 20, -20, 20,0,0+18),
graph( 500, 500, -20, 20, -20, 20,0,0+19))}}}




Here is a cleaner look at the intersection of regions





{{{drawing( 500, 500, -20, 20, -20, 20,
          graph( 500, 500, -20, 20, -20, 20,-(3/4)x+15,-x+18,1000(x-0),0),circle(0,0,0.1),
circle(0,2,0.1),
circle(0,4,0.1),
circle(0,6,0.1),
circle(0,8,0.1),
circle(0,10,0.1),
circle(0,12,0.1),
circle(0,14,0.1),
circle(2,0,0.1),
circle(2,2,0.1),
circle(2,4,0.1),
circle(2,6,0.1),
circle(2,8,0.1),
circle(2,10,0.1),
circle(2,12,0.1),
circle(4,0,0.1),
circle(4,2,0.1),
circle(4,4,0.1),
circle(4,6,0.1),
circle(4,8,0.1),
circle(4,10,0.1),
circle(6,0,0.1),
circle(6,2,0.1),
circle(6,4,0.1),
circle(6,6,0.1),
circle(6,8,0.1),
circle(6,10,0.1),
circle(8,0,0.1),
circle(8,2,0.1),
circle(8,4,0.1),
circle(8,6,0.1),
circle(8,8,0.1),
circle(10,0,0.1),
circle(10,2,0.1),
circle(10,4,0.1),
circle(10,6,0.1),
circle(12,0,0.1),
circle(12,2,0.1),
circle(12,4,0.1),
circle(14,0,0.1),
circle(14,2,0.1),
circle(16,0,0.1),
circle(0,0,0.1),
circle(0,2,0.1),
circle(0,4,0.1),
circle(0,6,0.1),
circle(0,8,0.1),
circle(0,10,0.1),
circle(0,12,0.1),
circle(0,14,0.1),
circle(2,0,0.1),
circle(2,2,0.1),
circle(2,4,0.1),
circle(2,6,0.1),
circle(2,8,0.1),
circle(2,10,0.1),
circle(2,12,0.1),
circle(4,0,0.1),
circle(4,2,0.1),
circle(4,4,0.1),
circle(4,6,0.1),
circle(4,8,0.1),
circle(4,10,0.1),
circle(6,0,0.1),
circle(6,2,0.1),
circle(6,4,0.1),
circle(6,6,0.1),
circle(6,8,0.1),
circle(6,10,0.1),
circle(8,0,0.1),
circle(8,2,0.1),
circle(8,4,0.1),
circle(8,6,0.1),
circle(8,8,0.1),
circle(10,0,0.1),
circle(10,2,0.1),
circle(10,4,0.1),
circle(10,6,0.1),
circle(12,0,0.1),
circle(12,2,0.1),
circle(12,4,0.1),
circle(14,0,0.1),
circle(14,2,0.1),
circle(16,0,0.1),
circle(0,0,0.1),
circle(0,2,0.1),
circle(0,4,0.1),
circle(0,6,0.1),
circle(0,8,0.1),
circle(0,10,0.1),
circle(0,12,0.1),
circle(0,14,0.1),
circle(2,0,0.1),
circle(2,2,0.1),
circle(2,4,0.1),
circle(2,6,0.1),
circle(2,8,0.1),
circle(2,10,0.1),
circle(2,12,0.1),
circle(4,0,0.1),
circle(4,2,0.1),
circle(4,4,0.1),
circle(4,6,0.1),
circle(4,8,0.1),
circle(4,10,0.1),
circle(6,0,0.1),
circle(6,2,0.1),
circle(6,4,0.1),
circle(6,6,0.1),
circle(6,8,0.1),
circle(6,10,0.1),
circle(8,0,0.1),
circle(8,2,0.1),
circle(8,4,0.1),
circle(8,6,0.1),
circle(8,8,0.1),
circle(10,0,0.1),
circle(10,2,0.1),
circle(10,4,0.1),
circle(10,6,0.1),
circle(12,0,0.1),
circle(12,2,0.1),
circle(12,4,0.1),
circle(14,0,0.1),
circle(14,2,0.1),
circle(16,0,0.1),
circle(0,0,0.1),
circle(0,2,0.1),
circle(0,4,0.1),
circle(0,6,0.1),
circle(0,8,0.1),
circle(0,10,0.1),
circle(0,12,0.1),
circle(0,14,0.1),
circle(2,0,0.1),
circle(2,2,0.1),
circle(2,4,0.1),
circle(2,6,0.1),
circle(2,8,0.1),
circle(2,10,0.1),
circle(2,12,0.1),
circle(4,0,0.1),
circle(4,2,0.1),
circle(4,4,0.1),
circle(4,6,0.1),
circle(4,8,0.1),
circle(4,10,0.1),
circle(6,0,0.1),
circle(6,2,0.1),
circle(6,4,0.1),
circle(6,6,0.1),
circle(6,8,0.1),
circle(6,10,0.1),
circle(8,0,0.1),
circle(8,2,0.1),
circle(8,4,0.1),
circle(8,6,0.1),
circle(8,8,0.1),
circle(10,0,0.1),
circle(10,2,0.1),
circle(10,4,0.1),
circle(10,6,0.1),
circle(12,0,0.1),
circle(12,2,0.1),
circle(12,4,0.1),
circle(14,0,0.1),
circle(14,2,0.1),
circle(16,0,0.1))}}} Here is the intersection of the 4 regions represented by the series of dots


Anywhere in this combined shaded region represents a point (x,y) which represents the number of AM and AM/FM radios that need to be produced to stay within the restrictions.