math

Problem 1 Consider a simple economy with three sectors, agriculture, manufacturing and energy. The production of 1 unit of agriculture requires the consumption of 0.2 unit if agriculture, 0.2 unit of manufacturing and 0.2 unit of energy. The production of 1 unit of manufacturing requires 0.4 unit of agriculture, 0.1 unit of manufacturing and 0.1 unit of energy. The production of 1 unit of energy requires the consumption of 0.3 unit of agriculture, 0.1 unit of manufacturing and 0.1 unit of energy. Find the level of production for each sector to satisfy the demand for 10 billion worth of agriculture, $15 billion worth of manufacturing and $20 billion of energy. Problem 2 A small manufacturing plant makes three types of inflatable boats: One person, two person and four person models. Each boat requires the services of three departments, as listed in the table below. The cutting assembly and packaging departments have available 380, 330 and 120 labor-hours per week, respectively How many of each type of boat must be produced each week for a plant to operate at full capacity Solution Problem 3 A fast food chain plans to expand by opening several new restaurants; the chain operates two types of restaurants, drive through and full service. A drive through restaurant costs $100,000 to construct, requires 5 employees and has expected annual revenue of $200,000. A full service restaurant costs of $150,000 to build, requires 15 employees and has an expected annual income of $500,000. The chain has $2,400,000 in capital available for expansion. Labor contracts require that they hire no more than 210 employees and licensing requirements require that they open no more than 20 new restaurants. Home many restaurants of each type should the chain open in order to maximize the expected revenue? What is the maximum expected revenue? How much of their capital will they use and how many employees will the hire?