price would drop from $$15$ per bracket to $$14\mathrm{.}50$ per bracket if Ross would purchase the brackets in lots of $1,000.$ Lead times, however, would increase to $3$ days for this larger quantity.$($a$)$ What is the total annual inventory cost plus purchase cost if Ross buys the brackets in lots of $1,000$ at $$14\mathrm{.}50$ each?$($b$)$ If Ross does buy in lots of $1,000$ brackets, what is the new ROP?$($c$)$ Given the options of purchasing the brackets at $$15$ each, producing them in$-$house at $$14\mathrm{.}80,$ and taking advantage of the discount, what isyour recommendation to Ross White?