Suppose your firm produces breakfast cereal and needs $215,000$ bushels of corn in July $2023$ for an upcoming promotion. You would $\backslash$table$[[$Agrlculture Futures$],[$Corn $($CBT$)-5,000$ bu; cents per bu$,,,,,,],[$May$,635\mathrm{.}75,638\mathrm{.}78,620\mathrm{.}00,633\mathrm{.}25,\mathrm{.}75,240],[$July$,581\mathrm{.}00,593\mathrm{.}75,572\mathrm{.}75,586\mathrm{.}25,4\mathrm{.}00,531,343]]$

like to lock in your costs today because you are concerned that corn prices might rise between now and July. Use Table $23\mathrm{.}1.$

a$.$ What total cost would you effectively be locking in based on the closing price of the day?

Note: Do not round intermediate calculations and round your answer to the nearest whole number, e$.$g$.,32.$

b$.$ Suppose corn prices are $$5\mathrm{.}63$ per bushel in July. What is the profit or loss on your futures position?

Note: Do not round intermediate calculations and enter your answer as a positive value rounded to the nearest whole number,

e$.$g$.,32.$