You would like to maximize profits at your bakery, which makes
decorated sheet cakes for parties in two sizes, a full sheet and a half
sheet. A batch of 12 full-sheet cakes takes 3.5 hours of oven time and
3 hours of decorating time, whereas a batch of 20 half-sheet cakes
takes 5 hours of oven time and 4 hours of decorating time. The oven
is available for a maximum of 21 hours a day, and the decorating
room is available for 14 hours a day. Let x represent the number of
batches of sheet cakes that the bakery produces in one day, and let y
represent the number of batches of half-sheet cakes. The bakery makes
a profit of $30 on each batch of full-sheet cakes and $35 on each
batch of half-sheet cakes.
a. Write a constraint about oven time.
b. Write a constraint about decorating time.
c. Write a system of inequalities that includes the constraints you have
found and any commonsense constraints.
d. Graph the feasible region and find the vertices.
e. Find the profit at each vertex.
f. How many batches of each size of cake should the bakery make in
one day to maximize profit? What is the maximum profit?