Question 1210283
<pre>
.
1. Graph 𝑅(𝑥). Label the axes in context. Show the
scale used for both the x- and y-axis.

{{{drawing(500,500,-2,10,-2,10, 
locate(.1,9.8,"R(x)"),
line(0,1,14,15),
line(-3,5,12,5), line(0,-3,0,12), 

locate(-1,.2,-250),
locate(-1,1.2,-200),
locate(-1,2.2,-150),
locate(-1,3.2,-100),
locate(-1,4.2,-50),
locate(-1,5.2,0),
locate(-1,6.2,50),
locate(-1,7.2,100),
locate(-1,8.2,150),
locate(-1,9.2,200),

locate(1,5,1),
locate(2,5,2),
locate(3,5,3),
locate(4,5,4),
locate(5,5,5),
locate(6,5,6),
locate(7,5,7),
locate(8,5,8),
locate(9,5,9),
locate(9.8,5.35,x),
line(-.1,0,.3,0),
line(-.1,1,.3,1),
line(-.1,2,.3,2),
line(-.1,3,.3,3),
line(-.1,4,.3,4),
line(-.1,5,.3,5),
line(-.1,6,.3,6),
line(-.1,7,.3,7),
line(-.1,8,.3,8),
line(-.1,9,.3,9)
)}}}

2. Find R(0) and interpret this value in context.

The point R(0) = (0,-200) represents the fact that we start out $200 "in the
hole" because in the beginning we haven't sold any units (0 units sold).

3. Determine how many units must be sold for
revenue to break even (𝑅(𝑥)=0).

The "break-even" point is the x-intercept, when the revenue R(x) = 0.

We set R(x) = 0
R(x) = 50x-200 = 0
           50x = 200
             x = 4

So the break-even point is (4,0).  It's when we've sold enough units to get us
"out of the hole", even though we haven't made a profit yet.  To break-even, we
need to have sold 4 units.

answer: 1. x-intercept (0,-200) y-intercept (4,0)
2 R(0)= -200
3. [R(x) = 0]; X=4 (units to be sold)

Edwin</pre>