Houseco Developers is considering erecting three office buildings. The time required to complete each and the number of workers required to be on the job at all times (during construction) are shown in the following table. All the buildings are started at the beginning of a year. Once a building is completed, it brings in the following amount of rent per year: building 1 , $50,000; building 2,$30,000; building 3 , $40,000. Houseco faces the following constraints: - During each year, 60 workers are available. - At most, one building can be started during any year. - Building 2 must be completed by the beginning of year 4 . (That is, it has to be started before year 3.) (a) (15 points) Formulate an integer program that will maximize the total rent earned by Houseco through the end of year 6. Define your decision variables clearly. (Hint: Obvisouly, you will not start a building in years 5 or 6.) (b) (10 points) Solve the model you developed in part (a) using OpenSolver and report the optimal solution. (Hint: Optimal objective function value is 370,000 )