Question 1 A cargo airplane has a compartment for storing cargo. This compartment has a weight capacity of 27 tons and a space capacity of 16,000 tons The following four cargo types have been offered for shipment on an upcoming flight as space is available: Cargo Weight (tons) Volume (cu ft)/ton Profit ($/ton) Apparel 14 500 100 Electronics 10 700 130 Hardware 18 600 105 Supplies 400 90 For example, there are up to 14 tons of apparel available, each ton takes up 500 cubic feet, and earns $100 in profit. Any portion of each of these cargoes can be accepted. The objective is to determine how much of each cargo type should be accepted and how to distribute each among the compartments to maximize the total profit for the flight. 1. Use the GOMP to define your model in words, including the objective, decision variables, and constraints. (10 points) 2. Use the GOMP to formulate your model mathematically, including the decision variables, objective function, and constraints. (10 points) 3. Now suppose that there is a fixed cost of $200 for each type of cargo you take on. Reformulate your mathematical model to reflect these costs. (7 points) 4. In addition to the fixed costs in c), suppose that you must take on at least two types of cargo, but no more than three types. Reformulate your mathematical model from c) to reflect these constraints. (3 points)