An antifreeze producer is faced with the decision to determine how much product to manufacture to meet demand during this year's winter season. Currently, the company has on hand an inventory of 250,000 gallons that were not sold last season. Demand in millions of gallons behaves as a random variable with a density function: f (X) = 1 for values of 1 ≤ X ≤ 2.

Accounting estimates have determined that each gallon produced in excess will have a storage cost of $ 0.50 for each unit inventoried until the following year. On the other hand, it is known that the production cost of a gallon is $ 1.5 per unit, while its selling price is $ 4.25 per unit. For simplicity, the producer considers that each missing unit will be penalized with an amount equivalent to the profit not obtained. Determine the following:

Point	Answer
Inventory model to apply in the solution	Model:
Demand during the selling season	X ~
The optimal number of gallons of antifreeze to produce for this season.	Q*=
The expected cost for this season's operation.	G(Q*)=