Two blocks of rubber with a modulus of rigidity $G=12$ MPa are bonded to rigid supports and to a plate $A B .$ Knowing that $c=100 \mathrm{mm}$ and $P=45 \mathrm{kN},$ determine the smallest allowable dimensions and $b$ of the blocks if the shearing stress in the rubber is not to exceed $1.4 \mathrm{MPa}$ and the deflection of the plate is to be at least $5 \mathrm{mm}$.