A horticulturist is considering growing five types of flowers to sell in retail stores. The flowers are (1) roses, which net a profit of $2.00 per flower, (2) carnations, which net a profit of $0.75 per flower, (3) daisies, which net a profit of $0.35 per flower, (4) chrysanthemums (mums), which net a profit of $0.25 per flower, and (5) daffodils, which net a profit of $0.70 per flower. The horticulturist owns 9 acres of land, which is suitable for growing any of these five flowers. Assume the horticulturist faces the following production technology:
Resource Requirement
Resource Unit Resource Roses Carnations Daisies Mums Daffodils Endowment
|
Acres per Flower
|
0.001
|
0.0005
|
0.0003
|
0.0001
|
0.0004
|
9
|
|
Hours of Labor
|
0.100
|
0.0700
|
0.0600
|
0.0500
|
0.0700
|
1,200
|
Further assume that (1) at most, 2,500 roses can be grown and (2) the combination of daisies and mums cannot exceed 5,000 flowers. The sole objective is to maximize profits. Find the optimal solution to this problem using the simplex method. Write out each simplex tableau, and show all your work in arriving at each tableau. Clearly label each tableau.