James and Jenn Smith have been tasked with making certain items for their church's bake sale scheduled for the following Sunday after Service. They have decided to make some combination of pound cakes, bread, blueberry pies, and sugar cookies. On Wednesday, Jenn went to the store and purchased 20 pounds of flour, 10 pounds of sugar, and 3 dozen eggs, which are the three main ingredients in all the baked goods they were thinking about making. The following table shows how much of each of the main ingredients is required for each baked good: Ingredients Flour (Cups) Sugar Cups) Eggs Baking Time (mins) Cake 2.5 2 2 45 Bread 9 0.25 0 35 Pie 1.3 1 5 50 Cookies 2.5 1 2 16 There are 18.5 cups in a 5-pound bag of flour and 12 cups in a 5-pound bag of sugar. James and Jenn plan to get up and start baking on Friday morning after their children board the school bus. and finish before they come back later that evening (8 hours later). They know that the Church will sell a pound cake for $12, a loaf of bread for $8, a blueberry pie for $10, and a batch of cookies for $6. Jenn wants to decide how many of each type of baked good she should make in order for the Church to make the most money possible. 1. Formulate a linear programming model for this problem. 2. Solve the linear programming model formulated in (a) above and answer these questions: a. Are any of the ingredients left over? b. If James and Jenn could get more of any ingredient, which should it be? Why? c. If they could get 6 more eggs, 20 more cups of flour, or 30 more minutes of oven time, which should they choose? Why? d. The solution values for this problem should logically be integers (can't have 0.3 eggs, right?). If the solution values are not integers, discuss how they should decide how many of each item to bake (how should she round the numbers, up, or down)? How do total sales for this integer solution compare with those in the original, non-integer solution?