9. Consider the problem of loading a cargo ship with 3 holds: the fore, center, and aft holds. These holds have both weight and volume capacities: Fore hold 2900 tons or 110,000 cu.ft. Center hold 3800 tons or 135,700 cuft. Aft hold 1550 tons or 44,000 cuft. There are 4 cargo types which can be mixed in different combinations and then loaded into the 3 holds. Data about these cargo types are tabulated below. Cargo type Density (tons/cult.) Unit prot ($/cu.ft.) Total weight (tons) 1 .48 45 6,000 2 .60 62.50 2,400 3 .27 3 8 3,900 4 .35 21.75 1,200 It is clear that such a ship must not be overloaded. In addition, however, the load must also be carefully distributed: the total weight loaded in any of the holds must be proportional to its weight capacity. That is, if one of the holds is loaded to 80% of its weight capacity, then so must the other two. Otherwise, the ship could be unstable. How should the three holds be loaded so as to maximize total prots? Formulate the problem as a linear programming