Consider a chocolate manufacturing company that produces only 3 types of chocolate: bittersweet chocolate, milk chocolate, and dark chocolate. Their ingredients are Sugar, Milk, and Choco.

To manufacture each type of chocolate, the following quantities are required:

• Each unit of bittersweet chocolate requires 3 units of milk, 2 units of choco and 4 units of sugar
• Each unit of milk chocolate requires 6 units of milk, 5 units of choco and 5 units of sugar
• Each unit of dark chocolate requires only 10 units of choco and 2 units of sugar (no milk is used for the dark chocolate)

The available amount of milk, choco and sugar is 100, 180, and 180, respectively. Assume the production levels must ensure the dark chocolate units are at least 5% of total production.

The profit margin for every unit of bittersweet chocolate, milk chocolate, and dark chocolate is $3, $3, and $6, respectively.

Formulate an LP model to determine the production level for each type of chocolate so as to the total profit is maximized.

Let B denote the unit number of produced bittersweet chocolate,

Let M denote the unit number of produced milk chocolate,

Let D denote the unit number of produced dark chocolate,