formulate a linear programming model

PittsBees is a small honey producer in Pittsburgh that operates three apiaries (where beehives are kept), two refineries, and three retail shops. Each bottle of honey starts as raw honey at an apiary, is processed and bottled at a refinery, and finally sold at a shop. In the coming year, PittsBees estimates that it will need to stock the following numbers of bottles at each of its shops: Shop 1 Shop 2 Shop 3 8,000 6,000 7,000 Each of the three apiaries can produce exactly 10,000 bottles worth of raw honey, and the two refineries have no limits on their processing and bottling capacity PittsBees goal is to stock each of its shops at minimum total shipping cost. The per- bottle shipping cost from each apiary to each refinery is given in the following table (we are just using "bottles" as a unit of volume here - raw honey does not actually ship in bottles from apiary to refinery): Apiary 1 Apiary 2 Apiary 3 Refinery 1 $0.50 $1.00 $1.50 Refinery 2 $1.00 $1.00 $1.00 Similarly, the per-bottle shipping cost from each refinery to each shop is given below: Shop 1 Shop 2 Shop 3 Refinery 1 $2.00 $0.75 $1.25 Refinery 2 $1.50 $1.25 $1.25