The Better Bread Bakery is famous for its breads. They make two kinds: “Sunshine”, a white bread and “Moonlight”, a large dark bread. The market for the famous breads is endless. Every Sunshine loaf sold brings a profit of $0.05 and each loaf of Moonlight bread brings a profit of $0.08. There is a fixed cost of running the bakery of $400 per day, regardless of the amount of bread baked.
The bakery is divided into two departments: baking and mixing, with limited capacity in both departments. In the baking department there are ten big ovens, each with a capacity of 140 baking sheets per day. It is possible to put ten loaves of Sunshine on each of these baking sheets, or five of the larger Moonlight breads. You can make any combination of the two breads on the baking sheets. Just keep in mind that each Moonlight loaf takes twice the space of a Sunshine loaf. The mixing department can mix up to 8000 loaves of Sunshine bread per day and 5000 loaves of Moonlight bread. There are two separate automatic mixers so there is no conflict between making the two kinds of dough.
Since the market for both types of breads is unlimited, the management of BBB has decided to find the best product mix. The question is how many loaves of each type of bread should be baked each day to produce the highest profit, given the physical limitations of the bakery.
Let S = Number of Loaves of Sunshine to Produce
Let M = Number of Loaves of Moonlight to Produce
Maximize Profit = $
S + $
M – $
S < Limit on Number of Loaves of Sunshine M < Limit on Number of Loaves of Moonlight 10 Big Ovens with a capacity of 140 baking sheets per day === > 1400 Sheets could be baked each day.
Each loaf of Sunshine will take 1/10 (or .10) of a Baking Sheet
Each loaf of Moonlight will take 1/5 (or .20) of a Baking Sheet
Baking Sheet Constraint:
M < Non-Negativity Constraint: S > 0 , M > 0