Answer
See explanation
Work Step by Step
The temperature at the end of the compression varies with the compression ratio as $$
T_2=T_1\left(\frac{v_1}{v_2}\right)^{k-1}=T_1 r^{k-1}
$$ since $T_1$ is fixed. The temperature rise during the combustion remains constant since the amount of heat addition is fixed. Then, the maximum cycle temperature is given by $$
T_3=q_{\text {is }} / c_v+T_2=q_{\text {in }} / c_v+T_1 r^{k-1}
$$ The smallest gas specific volume during the cycle is $$
v_3=\frac{v_1}{r}
$$ When this is combined with the maximum temperature, the maximum pressure is given by $$
P_3=\frac{R T_3}{v_3}=\frac{R r}{v_1}\left(q_{\text {in }} / c_v+T_1 r^{k-1}\right)
$$
