The members want to know how many of each item they should bake to maximize the money they make.
The members want to know how many of each item they should bake to maximize the money they make.
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter4: Linear Programming Models
Section: Chapter Questions
Problem 73P
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The honorary business fraternity at Tech is planning an all-day bake sale on Saturday of a home football
game as a charity fund-raising project. The members will bake cakes, cupcakes, and cookies in one
member’s apartment oven starting at 5 p.m. on Friday after the members get out of class until midnight.
All the items bake at the same temperature (350 degrees) but for different times—40 minutes for a
cake, 25 minutes for cupcakes, and 8 minutes for cookies—so they will bake one item at a time. The
oven has enough space to bake a batch of 12 cakes or 48 cupcakes or 60 cookies at a time. The recipe
for a cake calls for 2 eggs, 0.5 cups of butter, 1.5 cups of flour, and 1 cup of sugar. A batch of 12
cupcakes requires 2 eggs, 0.5 cups of butter, 1.5 cups of flour, and 1 cup of sugar; and the recipe for a
batch of 60 cookies calls for 2 eggs, 1 cup of butter, 2 cups of flour, and 1 cup of sugar. A local grocery
store has donated 10 dozen eggs and 30 pounds each of butter, sugar, and flour. (1 pound of butter
equals 2 cups, 1 pound of sugar equals 2.4 cups, and 1 pound of flour equals 4 cups). The members plan
to sell cakes for $15 apiece, cupcakes for $3 apiece, and cookies for $2 apiece. The members want to
know how many of each item they should bake to maximize the money they make.
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