Weekly customer demand for Amour du jour at a typical Amber restaurant is uniformly distributed between 200 gallons and 500 gallons. An Amber restaurant spends $75 per gallon to purchase the main raw materials needed for making Amour du jour from a local third-party supplier. It also charges 12 dollars per customer orders glass. The size of the glass for each order is 5.12 ounces or 0.04 gallons. So, Amber can serve 25 customer orders with one gallon of Amour du jour.

Any purchased raw materials that are not used to make Amour du jour by the end of the week will perish and must be thrown away. Vijay wants to help its restaurants that are split between two opposing decisions:

• Ordering raw materials for making more gallons of Amour du jour can lead to more sales, but it can become costly due to the spoilage of the unused materials.

• Ordering raw materials for making a lower number of gallons of Amour du jour can prevent some costs due to materials spoilage, but it can lead to stockout and lost profits.

  Vijay asks for help from your team with determining the orders for ingredients for the optimal number of gallons of Amour du jour per week.

Problem

• Formulate the profit function for Vijays ordering problem.

• What is the decision variable?

• Determine the optimal number of gallons of Amour du jour for which Amber must order

  raw materials each week to maximize the restaurants profit. What is the optimal profit?