ANSWER:
1. $2650, $26.5 per DVD
2.
STEP-BY-STEP EXPLANATION:
We have that the cost of the DVD is given by a function per part, for when there are 1000 or fewer units or when there are more than 1000. Just like this:
[tex]C(x)=\begin{cases}2500+1.5x,\text{ if x }\leq1000 \\ 2500+1.25x,\text{ if x }>1000\end{cases}[/tex]
1.
Now in this case we are going to produce 100 DVDs so we use the first equation, just like this:
[tex]\begin{gathered} C(100)=2500+1.5\cdot100 \\ C(100)=2500+150 \\ C(100)=2650 \end{gathered}[/tex]
Now, since he does not want to make a profit, he must charge the same value as the cost, in order to reach the break-even point, which means that he must charge the friend $2650
The cost per DVD is calculated by dividing the total cost by the number of DVDs, just like this
[tex]\begin{gathered} c=\frac{2650}{100} \\ c=26.5 \end{gathered}[/tex]
Which means the cost is $26.5 per DVD
2.
We calculate for each case:
[tex]\begin{gathered} C(0)=0 \\ c=x \\ \\ C(10)=2500+1.5\cdot10=2515 \\ c=\frac{2515}{10}=251.5 \\ \\ C(100)=2500+1.5\cdot100=2650 \\ c=\frac{2650}{100}=26.5 \\ \\ C(1000)=2500+1.5\cdot100=4000 \\ c=\frac{4000}{1000}=4 \\ \\ C(10000)=2500+1.25\cdot10000=15000 \\ c=\frac{15000}{10000}=1.5 \\ \\ C(100000)=2500+1.25\cdot100000=127500 \\ c=\frac{127500}{100000}=1.275 \\ \\ C(1000000)=2500+1.25\cdot1000000=1252500 \\ c=\frac{1252500}{1000000}=1.2525 \end{gathered}[/tex]
We replace each value in the table and we would be left with:
