= Solution
Let the third profit coefficient be $c_3$. For the same <basis>, the resource dual prices solve $2y_1+y_2=3$ and $5y_1+3y_2=c_3$, giving
$$
y_1=9-c_3,\qquad y_2=2c_3-15.
$$
Dual feasibility requires $y_1,y_2\ge0$ and $3y_1+2y_2\ge4$. These inequalities are $c_3\le9$, $c_3\ge15/2$ and $c_3\ge7$, respectively. Hence
$$
\boxed{15/2\le c_3\le9.}
$$
The production <vector> is unchanged because the resource constraints are unchanged. Equality at a boundary can allow additional optimal solutions.
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