Question: The Wisham family lives on a farm in South Georgia on which it produces a variety of crops and livestock, including pecans. It has 5 acres of pecan trees that yield approximately 1,000 pounds of unshelled pecans per acre each year. The family uses all of its pecan harvest to produce pecan pies, cookies, 1-pound bags of shelled pecans, and 5-pound bags of unshelled pecans, which it sells in town at the local farmers' market. The family sells pies for $5, packages of a dozen cookies for $3, bags of shelled pecans for $7, and bags of unshelled pecans for $16. A shelled pecan is half the weight of an unshelled pecan. It requires 4 ounces of shelled pecans to make a pie, and 6 ounces of shelled pecans to make a dozen cookies. The pies and cookies are baked in the family oven, and there are 120 hours of baking time available. It takes 55 minutes to bake a batch of 4 pies and 15 minutes to bake a batch of 2 dozen cookies. It requires family members 6 minutes to shell the pecans for a pie and package it, 4 minutes to shell the pecans for cookies and to package them, 10 minutes to shell the pecans for a 1 lb. bag of shelled pecans and package them, and 1 minute to package a bag of unshelled pecans; and there are 300 hours available from family members for shelling and packaging. The Wisham family wants to know how many pecan pies, dozens of cookies, and bags of shelled and unshelled pecans to produce in order to maximize its sales revenues.
(1). Formulate a linear programming model for this problem.
(2). Solve the LP in Excel.