LeSean Smith has made a deal with a restaurant to make some bakery to deliver on Saturday. He has decided to make some combination of chocolate chip cakes, loaves of Italian bread, custard pies, and pumpkin spice cookies. Thursday evening, he goes to the store and purchases 20 pounds of flour, 10 pounds of sugar, and 3 dozen eggs, which are the three main ingredients in all the baked goods he is thinking about making. The following table shows how much of each of the main ingredients is required for each baked good: There are 18.5 cups in a 5-pound bag of flour and 12 cups in a 5-pound bag of sugar. LeSean plans to get up and start baking on Friday morning after his kids leave for school and finish before they return after soccer practice (8 hours). He knows that the PTA will sell a chocolate chip cake for $12, a loaf of bread for $8, a custard pie for $10, and a batch of pumpkin spice cookies for $6. LeSean wants to decide how many of each type of baked good he should make for the local restaurant to make the most money possible. a) Formulate and solve a linear programming model for this problem. Your answer should report the followings: an LP model, the report of the optimal solution to the LP model: the values of the decision variables, and of the objective function. (55 pts) b) Are any of the ingredients left over? (15 pts) c) If LeSean could get more of any ingredient, which should it be? Why? (15 pts) d) If LeSean could get 6 more eggs, 20 more cups of flour, or 30 more minutes of oven time, which should he choose? Why? (15 pts)