20 points! can someone do part a for me? i know how to do these questions i’m just a tad bit confused. : /

Revenue = (number of phones)(price of phones)

If Mobistar charges $80 per phone, then their revenue is



If they instead charge $2 less per phone (so that ), or $78 per phone, then their revenue would be



If they charge $4 less per phone (), then they make



and so on. As the hint suggests, we can write the number of phones sold as an expression depending on the number of price decreases ; that is, for each price decrease, the number of phones sold increases by 40.

Similarly, the price per phone can be written in terms of , since the cost of a phone starts at a fixed $80 and decreases by $2 for each unit of . So total revenue can be written as



You can stop there, but you may be expected to write this in standard quadratic form, which is just a matter of expanding .



For the remaining parts:

(B) Writing in vertex form will help, as the name suggests. That's just a matter of completing the square. You have







which is to say the vertex of the parabola described by occurs at (10, 72,000). The parabola "opens downward" (which we know because the sign of the leading (quadratic) term is negative), so the vertex is a maximum of the revenue function, which in turn means the most revenue the company can achieve will be achieved if , netting them $72,000. This translates to setting the price per phone to .

Is there a picture?