A rigid square foundation is designed to carry the shown eccentric load. During soil exploration program an electric power transmission cable was found two meters below the ground surface. The maximum allowble vertical stress the cable can endure is $200$ kPa $.$ The foundation was also tied by infinite strength cable on the left edge

The foundation system is designed such that all of the system components are fully supported and can carry the load safely. Know that the cable and force are eccentric in the B direction only:

a$-$ Determine the factor of safety of the foundation for the geotechnical capacity to maintain the system at the allowable limits

b$-$ Determine the minum force to be exerted on the cable to maintain a factor of safety of $3\mathrm{.}0$

c$-$ Determine the maximum force that can be exerted on the cable

d$-$ Estimate the depth of exploration for case $($a$)$