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. Note that the number of Type 2 layouts cannot exceed the number of Type 1 layouts and there must be at least five layouts of each type. The greenhouse operator wants to know how many layouts of each type should be used to yield maximum profit. 

Formulate an IP to maximize profit and solve using LINDO/LINGO (or another optimization solver). Describe the optimal solution briefly.

Hint: Use the following decision variables: Li = number of type i layouts produced

Answer rating: 100% (QA)

Solution The integer programming IP model can be formulated as follows Maximize 50L1 30L2 60L3 Subje... View the full answer