Tricolore

Tricolore is an apparel retailer in east Austin, TX that sells mostly t$-$shirts and jeans. Tricolore$$s most popular item is a cotton t$-$shirt that comes in three colors: green, white, and red. Tricolore steadily sells about $300$ t$-$shirts of each color per month, and holds about a $1$ week supply of inventory of each color in stock $($i$.$e$.,75$ t$-$shirts$),$ on average. Tricolore buys each of the three t$-$shirts from a different supplier. All three suppliers charge Tricolore $$40$ per t$-$shirt ordered, but they differ in their shipment fees$$which Tricolore has to pay regardless of the size of the order. The green$-$t$-$shirt supplier charges a $$300$ delivery fee, the white$-$t$-$shirt supplier charges a $$200$ delivery fee, and the red$-$t$-$shirt supplier charges a $$400$ delivery fee. Tricolore$$s cost of holding inventory is high: $$8$ per t$-$shirt per month.

The goal of the problem is to help Tricolore with its inventory management.

a$.$ On average, how much cost is Tricolore incurring per month for holding inventory of each color t$-$shirt? On average, how much is Tricolore spending per month on delivery fees for each color of t$-$shirt? Does Tricolore hold the right amount, too little, or too much inventory for each t$-$shirt? Why?

b$.$ What order size would you recommend Tricolore adopts for each color t$-$shirt? Under the policy you recommend, how much inventory of each color t$-$shirt will Tricolore hold, on average?

c$.$ Tricolore was approached by a new supplier who carries all three colors. This supplier will charge Tricolore $$400$ per delivery but can deliver all three colors together, in a single shipment. Moreover, the variable cost $($the $$40)$ is up for negotiation. The holding cost per unit will still be $$8/$ month. What is the absolute maximum variable price Tricolore should accept? Why?