#### Answer

a. $\begin{cases} y \ge 0 \\x+y\geq5 \\ x\geq1 \\200x+100y\leq700 \end{cases}$
b. See graph; triangle where the corners are labeled.
c. $2$.

#### Work Step by Step

a. Based on the given conditions, we can write the inequality as
$\begin{cases} y\ge 0 \\x+y\geq5 \\ x\geq1 \\200x+100y\leq700 \end{cases}$
b. See graph; the solution of the above inequalities is the triangular region where the corners are labeled.
c. Based on the graph, we can determine that the greatest number of nights that can be spent at a large resort is $2$.