2. Alice's bakery produces bagels and muffins:
? to make a dozed bagels Alice needs 5 cups of flour, 2 eggs, and one cup of sugar;
? to make a dozen muffins Alice needs 4 cups of flour, 4 eggs, and two cups of sugar. Bob can
sell the bagels at $ 12/dozen and the muffins at $ 15/dozen.
In her kitchen, Alice has 50 cups of flour, 30 eggs and 20 cups of sugar. We want to determine how
many bagels and muffins should Alice make (without having to buy more ingredients!) in order to
maximize her potential total revenue.
(a) this problem has two unknowns. What are these?
(b) In terms of the variables, what is the objective function and what are the constraints?
(c) Draw the solution set of the constraints of the problem, in the Cartesian plane (it should be a
polygon).
(d) As the objective function is linear, its maximum value should be attained at a corner of the
constraint set. Find the coordinate of this corner to solve Alice's production problem.
