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.

In Problem $7,$ how much flour and sugar will be left unused if the optimal numbers of cakes and

Danish are baked?