IE 310: Operations ResearchMidterm Review Problems•Solutions will NOT be posted for these problems.You are encouraged to work out thesolutions for these problems and raise doubts during office hours if there are any.1. A cargo airplane has three compartments for storing cargo: front, center, and back. Thesecompartments have capacity limits on both weight and space as summarized below:CompartmentWeight capacity (tons)Space capacity (cubic feet)Front127,000Center189,000Back105,000Furthermore, the weight of the cargo in the respective compartments must be the sameproportion of that compartment’s weight capacity to maintain the balance of the airplane.The following four cargoes have been offered for shipment on an upcoming flight:CargoWeight (tons)Volume (cubic feet/ton)Profit (dollar/ton)120500320216700400325600360413400290Any portion of these cargoes can be accepted. Moreover, each cargo can be split between twoor more compartments if desired. The objective is to determine how much (if any) of eachcargo should be accepted and how to distribute each among the compartments in order tomaximize the total profit for the flight. Formulate this as a linear programming problem.2. Consider the following LP:maxZ= 2x1-x2x1+x2≥1x1-x2≤13x1+x2≤6x1, x2≥0(a) Is the LP in standard form? If not, write the standard form of the LP.(b) Draw the feasible region.