The Crumb and Custard Bakery makes coffee cakes and Danish pastries in large pans. The main ingredients are flour and sugar. There are 25 pounds of flour and 16 pounds of sugar available, and the demand for coffee cakes is 5. Five pounds of flour and 2 pounds of sugar are required to make a pan of coffee cakes, and 5 pounds of flour and 4 pounds of sugar are required to make a pan of Danish. A pan of coffee cakes has a profit of $1, and a pan of Danish has a profit of $5. Determine the number of pans of cakes and Danish to produce each day so that profit will be maximized.
a. Formulate a linear programming model for this problem.
b. Solve this model by using graphical analysis.