You are going to make and sell bread. a loaf of irish soda bread is made with 2 c flour and 1/4 c sugar. kngelhopf cake is made with 4 c flour and 1 c sugar. you will make a profit of $1.50 on each loaf of irish soda bread and a profit of $4 on each kugelhopf cake. you have 16 c flour and 3 c sugar. a.) how many of each kind of bread should you make to maximize the profit? b.) what is the maximum profit? show the formulas .

A)  You should make 4 loaf of Irish soda bread and 2 Kugelhopf cake to maximize the profit.

B)  The maximum profit is $14.

Explanation

Suppose, you should make loaf of Irish Soda Bread and loaf of Kugelhopf cake.

A loaf of Irish soda bread is made with 2 c flour and 1/4 c sugar. So, the amount of flour in loaf of bread is c and the amount of sugar is c.

Kngelhopf cake is made with 4 c flour and 1 c sugar. So, the amount of flour in loaf of bread is c and the amount of sugar is c.

You have total 16 c flour and 3 c sugar. So, the constraints will be.......

You will make a profit of $1.50 on each loaf of Irish Soda Bread and a profit of $4 on each Kugelhopf cake. So, the profit function will be:  

If we graph the above constraints, then the vertices of the common shaded region will be:   and  (Please refer to the below image for the graph)

For ,  

For ,  

For ,  

For ,  

So, the profit will be maximum, when   and

Thus, you should make 4 loaf of Irish soda bread and 2 Kugelhopf cake to maximize the profit.

The maximum profit will be $14