Suppose you launch an online business in order to capitalize on the boom in online shopping due to the current pandemic. Your online store sells various types of breath mints, some of which you invented and marketed yourself! You named your most popular breath mint invention Mintos. You are trying to minimize annual inventory costs for Mintos. You sell 1500 packs of Mintos each year, and it costs $1.25 to store each pack for one year. To reorder a shipment of Mintos, you need to pay a flat fee of $30 plus $0.12 per packet of Mintos. You will reorder shipments of Mintos N times each year for a total of 1500 packets. Each order will have the same lot size of x packets of Mintos.

(a) Write down a formula for the yearly storage cost if you order x packets of Mintos N times each year. Show your work!

(b) Write down a formula for the yearly reordering cost if you order x packets of Mintos N times each year. Show your work!

(c) Use your answers to (a) and (b) to write down a simplified formula for the yearly inventory costs C(x) related to storing and ordering Mintos. Show your work! C(x) =

(d) Since the lot size for each shipment will always be somewhere between 1 and 1500 packets of Mintos, locate any critical values for C(x) in the interval [1, 1500]. Show your work! Round to two decimal places, if necessary. Critical value(s) at x =

(e) Determine the absolute maximum and absolute minimum yearly inventory costs for x in the interval [1, 1500]. Show your work!

Absolute max cost of dollars when x =

Absolute min cost of dollars when x =