Amanda, a hairstylist based in New York had to stop working temporarily due to a lice outbreak. She started to make two types of children's wooden toys in her basement, cars (C) and dolls (D). Cars yield a contribution margin of $9 each and dolls have a contribution margin of $8 each. Since her electric saw overheats, Amanda can make no more than 7 cars or 14 dolls each day. Since she doesn't have equipment for drying the lacquer finish that she puts on the toys, the drying operation limits her to 16 cars or 8 dolls per day. Amanda wants to know what is the combination of cars and dolls that she should make each day to maximize her profits, subject to her constraints.

a) Formulate a linear programming problem to depict Amandas objective algebraically.

b) What are the corner points in Amandas feasible region?

c) Solve this problem using the corner point method. Find the optimal combination of cars and dolls. What is the optimal profit at that combination?