b$)$ For the value of order quantity Q$,$ you can round it to the nearest integer.

$(25$ points$)$ You start a t$-$shirt business, where you sell red and blue shirts. There is a steady demand of $280$ red shirts per year and $220$ blue shirts per year. Supplier $1$ will sell you shirts of either color at $$4$ each, and will charge an additional $$1600$ thsetup an order regardless of the quantity and color$($s$)$ of shirts purchased. Supplier $2$ only stocks red shirts and sells them for $$3\mathrm{.}60$ each, and charges an addition $$100$ to setup an order. Order fulfillment isn't immediate and orders from either supplier take one year to arrive. All demand must be fulfilled.

Assume a $10\%$ annual interest rate.

$($a$)$ If you were to decide to order each color of shirt from the cheapest supplier, how many red shirts should you request per order, how often would you place an order for red shirts, and at what inventory level of red shirts should each order be placed?

$($b$)$ Under the same strategy given in part $($a$),$ how many blue shirts would you request per order, how often should you place an order for blue shirts, and at what inventory level of blue shirts should each order be placed?

$($c$)$ If you decide to order all your shirts from the same supplier, allowing you to place orders containing both colors of shirts $($while still only paying one setup cost per order$),$ how many shirts should you request per order, and how often would you place an order?

$($d$)$ Under the strategy given in part $($c$),$ what fraction of shirts per order should be red, and what fraction should be blue? Hint: this should be an easy problem; ignore rounding issues and don't overthink it$!$