The break-even point is the point at which there is no loss or gain in business. For n = 2 , $2 price increases will be break even.
Break-even point is the point at which total revenue equals total costs . At this point there is no profit or loss.
Projected profit model is,
[tex]P(n) = -10n^2 + 50n + 7,500[/tex]
where n is the number of $2 price increases
Since at break even, there is no profit
So, equate P(n) = 0
[tex]0= -10n^2 + 50n + 7,500\\\\n^2 - 5n - 7,50=0\\\\n^{2} -30n+25n-750=0\\\\(n-30)(n+25)=0\\\\n=-25,n=30[/tex]
Since, n is the number of $2 price increases . So it can not be negative
Therefore, n = 30
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