Video Transcript
A company produces lollipops. In the equations 𝐶 of 𝑥 equals
3000 plus three over two 𝑥, 𝑅 of 𝑥 equals two of 𝑥, the function 𝐶 of 𝑥
represents the total production cost, in dollars, of 𝑥 lollipops. And the function 𝑅 of 𝑥
represents the total revenue, in dollars, from selling 𝑥 lollipops. How will the total cost of
producing the lollipops change if the number of produced lollipops increases by 1000
units?
Since we know that we’re
considering the total cost of producing the lollipops, we’re interested in the first
equation 𝐶 of 𝑥 equals 3000 plus three-halves 𝑥. In this equation, we have a
constant value of 3000. This value is not dependent on how
many lollipops you make. And then, we have the three-halves
𝑥, which gives us the cost per lollipop. If we added 1000 more units, it
would cost three-halves times 1000, which is 3000 over two or 1500. And so we say the total cost will
increase by 1500 dollars.
Let’s consider another way to solve
this problem or a way to check what we’ve already done. We could calculate the cost of
making one lollipop, a constant 3000 plus three-halves times one. When we do that multiplication, we
see that it costs 3001 dollars and 50 cents. Now we want to increase the number
produced by 1000 units. So we’ll calculate the cost of
producing 1001 units, a constant 3000 plus three-halves times 1001. This gives you 4501 dollars and 50
cents. And 4501 dollars and 50 cents minus
3001 dollars and 50 cents equals 1500 dollars. Again, an increase of 1500
dollars.
