students stuff envelopes for extra money

Question

Students stuff envelopes for extra money. Their initial cost to obtain the information for the job was ​$100.

Each envelope costs ​$0.03 and they get paid ​$0.04

per envelope stuffed. Let x represent the number of envelopes stuffed.

​(a) Express the cost C as a function of x.

​(b) Express the revenue R as a function of x.

​(c) Determine analytically the value of x for which revenue equals cost.

Answer 1

Let's consider the cost function first. There is an initial cost of $100. This is fix and will not change. There is a cost of $0.03 per envelope. This variable cost will be 0.03x, where x is the number of envelops stuffed. This gives us a cost function of

C(x) = 0.03x + 100

The revenue function is straight forward. The students earn $0.04 per envelop stuffed, or 0.04x. This gives us a revenue function of

R(x) = 0.04x

Now to determine the value of x where the revenue equals the cost we simply set the two expressions equal.

0.04x = 0.03x + 100 (subtract 0.03x from both sides)

0.01x = 100 (divide both sides by 0.01)

x = 10000

The students would have to stuff 10000 envelops to break even.