A student stuffs envelopes for extra income during her spare time. Her initial cost to obtain the necessary information for the job was ​$120. Each envelope costs ​$0.06 and she gets paid ​$0.07 per envelope stuffed. Let x represent the number of envelopes stuffed.

Question

​(a) Express the cost C as a function of x.
​(b) Express the revenue R as a function of x.
​(c) Determine the value of x for which revenue equals cost.
​(d) Graph the equations y=​C(x) and y=​R(x) on the same​ axes, and interpret the graph.
Question content area bottom
Part 1
​(a)​ C(x)=enter your response here ​(C in​ dollars)
​(Use integers or decimals for any numbers in the​ expression.)
Part 2
​(b)​ R(x)=enter your response here ​(R in​ dollars)
​(Use integers or decimals for any numbers in the​ expression.)
Part 3
​(c) Revenue equals cost when x=enter your response here.
​(Type an integer or a​ decimal.)
Part 4
​(d) Choose the correct graph below that represents y=​C(x) and y=​R(x).
A.
0
20,000
0
1500
x
y


A coordinate system has a horizontal x-axis labeled from 0 to 20000 in increments of 2000 and a vertical y-axis labeled from 0 to 1500 in increments of 150. A line that rises from left to right passes through the points (0, 120) and (10000, 720). A line that rises from left to right passes through the points (0, 0) and (10000, 1050). The lines intersect at approximately (2667, 280).
B.
0
20,000
0
1500
x
y


A coordinate system has a horizontal x-axis labeled from 0 to 20000 in increments of 2000 and a vertical y-axis labeled from 0 to 1500 in increments of 150. A line that falls from left to right passes through the points (0, 120) and (2000, 0). A line that rises from left to right passes through the points (0, 0) and (10000, 1050). The lines intersect at approximately (727, 76).
C.
0
20,000
0
1500
x
y


A coordinate system has a horizontal x-axis labeled from 0 to 20000 in increments of 2000 and a vertical y-axis labeled from 0 to 1500 in increments of 150. A line that falls from left to right passes through the points (0, 120) and (2000, 0). A line that rises from left to right passes through the points (0, 0) and (10000, 700). The lines intersect at approximately (923, 65).
D.
0
20,000
0
1500
x
y

Answer 1

The correct choice is D. A coordinate system has a horizontal x-axis labeled from 0 to 20000 in increments of 2000 and a vertical y-axis labeled from 0 to 1500 in increments of 150. A line that falls from left to right passes through the points (0, 120) and (2000, 0). A line that rises from left to right passes through the points (0, 0) and (10000, 700). The lines intersect at approximately (923, 65).

This graph represents the cost function, C(x), and revenue function, R(x). The intersection point of the two lines represents the value of x for which revenue equals cost. The graph shows that initially, as the number of envelopes stuffed increases, the cost increases linearly, while the revenue increases at a slower rate. However, at a certain point, the revenue surpasses the cost, and the graph begins to show a positive slope. This indicates that after a certain number of envelopes stuffed, the student will start making a profit.