A ten-acre slum in New York City is to be cleared. The officials of the city must decide on the redevelopment plan. Two housing options are to be considered: x1 : low-income units and x2 : middle-income units. The types of housing can be developed at 20 and 15 units per acre respectively. The unit costs of the low-income and middle-income housing are $13,000 and $18,000 respectively. One objective is to minimize the overall cost of the development. The lower and upper limits set by the officials on the number of low-income housing units are 60 and 100. Similarly, the number of middle-income units must lie between 30 and 70. The combined maximum housing market potential is estimated to be 150 (which is less than the sum of the individual market limits due to the overlap between the two markets). The total mortgage committed to the renewal plan is not to exceed $2 million. Finally, it was suggested by the architectural adviser that the number of low-income housing units be at least 50 units greater than one-half the number of middle-income units. Another objective suggested by the developer was to maximize the number of low income and middle-income units built subject to the same set of constraints where the minimal cost solution was to be considered.
[a] Formulate the multi-objective housing renewal model as a Linear Vector Optimization problem.
[b] Solve the above problem and generate the noninferior extreme points, edges and faces of the problem by whatever method you deem appropriate.