In a small city with a population of approximately 20,000 inhabitants. The annual tax base for property tax amounts to $ 550 million. Annual collections for food and medicine as well as for general sales are $ 35 and $ 55 million, respectively. Annual local gasoline consumption is estimated at 7.5 million gallons. The city council wants to develop tax rates based on four main goals: M1 Tax revenue must be at least $ 16 million to meet the city's financial commitments. M2 Food and medicine taxes should not exceed 10% of all taxes collected. M3 General sales taxes must not exceed 20% of all taxes collected. M4 Gasoline tax must not exceed 2 cents per gallon. Let the variables x_p, x_f, and x_s be the tax rates (expressed as proportions of the tax bases) on property, food, and general sales, and define the variable x_g as the gasoline tax in cents per gallon a) Formulate as a goal programming model. b) Solve the problem. Which solution method is more convenient? Justify your answer, define the objective function (s) and explain the solution obtained.