A refinery can blend $2$ raw materials into $2$ different products. At present, the management is

trying to decide how much of each of the raw materials to purchase and stock, so that they can

be blended to satisfy the demand for the products in a future time period, for which the demand

of the products is unknown. The demand has to be completely satisfied, and in case of raw

material shortage the products can be outsourced at a higher cost. There is an inventory

constraint on how much raw material can be stocked in total and any raw material not used will

be lost. Consider the following problem data:

$$ Producing a unit of product A$,$ requires $5$ units of the first raw material and $4$ units of the

second raw material.

$$ Producing a unit of product B$,$ requires $6$ units of the first raw material and $3$ units of the

second raw material.

$$ The cost of the raw materials is $$5$ and $$7,$ respectively. The maximum storage capacity for

raw materials is $1000$ units.

$$ The demand is estimated to be distributed N$($mean$=20,$ std$=5)$ for product A$,$ and N$($mean$=25,$

std$=10)$ for product B$.$ The cost of outsourcing is $$100$ for both products.