For the doubly$-$reinforced beam section shown below, determine the $A_s^{\text{'}}$ and $A_s$ required to carry a service live load moment of $500$kips$-ft$ and a service dead load moment of $250$ kips$-$ft$.$ Use the iterative approach suggested in your textbook to verify that the design is appropriate to carry the ultimate moment. Verify that your designed section is tension$-$controlled. Do all necessary checks to have a suitable design. Use $f_c^{\text{'}}=4800$ and $f_y=60000.$