Kathleen, a hairstylist based in Edmonton had to stop working temporarily due to the health and safety restrictions imposed by the government due to the COVID 19 crisis. 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, Kathleen 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. Kathleen 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 Kathleen's objective algebraically.

b) What are the corner points in Kathleen's 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?