The Charm City 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. The demand for coffee cakes is less than or equal to 4. 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 pastries. A pan of coffee cakes has a profit of $4, and a pan of Danish pastries has a profit of $6. Determine the number of pans of cakes and Danish pastries to produce each day so that profit will be maximized.
(a) Formulate a linear programming model for this problem.
(b) Find the optimal solution of this model by hand using the corner points graphical method.