18. Odie Dumon raises grapes to sell to wine makers. He just purchased an 80-acre plot on which he intends to plant grape vines. Although the species are the same, the size of the grapes can be controlled to be either large or small through differ- ent branch pruning methods and fertilizers.

On average, an acre of large grapes will yield 120 kilograms and require 3 labor hours to harvest. An acre of small grapes will yield 200 kilograms of small grapes with 4.5 labor hours to harvest. Odie can sell a kilogram of large grapes for $5.50. Small grapes bring $3.80 per kilogram of small grapes to wine makers. He has 260 labor hours for harvest available.

a. Formulate a linear program model to help Odie Duman know how many acres of small and large grapes to produce in order to maximize his profit. (Define decision variables and write the objective function and constraints.)

Formulate the problem in a textbox alongside the spreadsheet model. Place the optimal solution and optimal value in a separate textbox and state which constraints are binding.