Formulate the following as a linear programming problem: A greenhouse operator plans to bid for the job of providing flowers for city parks. He will use tulips, daffodils, and flowering shrubs in three types of layouts. A Type 1 layout uses 30 tulips, 20 daffodils, and 4 flowering shrubs. A Type 2 layout uses 10 tulips, 40 daffodils, and 3 flowering shrubs. A Type 3 layout uses 20 tulips. 50 daffodils, and 2 flowering shrubs. The net profit is $50 for each Type 1 layout, $30 for each Type 2 layout, and $60 for each Type 3 layout. He has 1,000 tulips. 800 daffodils, and 100 flowering shrubs. How many layouts of each type should be used to yield maximum profit? Explain how your formulation in the problem changes if both of the following conditions are added: a) The number of Type 1 layouts cannot exceed the number of Type 2 layouts. b) There must be at least five layouts of each type