Solution:
Given:
[tex]\begin{gathered} R=-28x^2+360x+29000 \\ C=300x+1100 \\ \\ x\text{ is the number of apartments} \end{gathered}[/tex]Profit is the surplus left from revenue after paying all costs.
Profit is found by deducting total costs from revenue.
Therefore, profit = total revenue - total costs.
Hence, the profit polynomial is gotten by;
[tex]\begin{gathered} P=R-C \\ P=(-28x^2+360x+29000)-(300x+1100) \\ P=-28x^2+360x+29000-300x-1100 \\ P=-28x^2+360x-300x+29000-1100 \\ P=-28x^2+60x+27900 \end{gathered}[/tex]Hence, the profit polynomial is;
[tex]P=-28x^2+60x+27900[/tex]The profits earned if 40 units are rented is;
[tex]\begin{gathered} x=40 \\ \\ P=-28x^2+60x+27900 \\ P=-28(40^2)+60(40)+27900 \\ P=-28(1600)+2400+27900 \\ P=-44800+30300 \\ P=-14500 \\ \text{But the model can not be negative,} \\ \\ \text{Hence, the profit is 14500} \end{gathered}[/tex]Therefore, the profit earned on 40 rented apartments is 14,500