Question

In: Statistics and Probability

A book publisher is planning to produce a book in three different bindings: paperback, book club...

A book publisher is planning to produce a book in three different bindings: paperback, book club and library. A paperback takes 2 minutes to sew, 4 minutes to glue, and sells for a profit of 25 cents. A book club edition takes 2 minutes to sew, 6 minutes to glue, and sells for a profit of 40 cents. A library edition takes 3 minutes to sew, 10 minutes to glue, and sells for a profit of 60 cents. The sewing process is available for 7 hours per day and the gluing process for 11 hours per day. How many books of each binding should the manufacturer make on a given day to maximise her profits?

Solutions

Expert Solution

Decision variables:
x = Number of paperback books
y = Number of bookclub books
z = Number of library books
P = Profit in $
Objective function:
Maximize P = 0.25x + 0.4y + 0.6z
Constraints:
2x + 2y + 3z ≤ 420 [Sewing time]
4x + 6y + 10z ≤ 660 [Glueing time]
x, y, z ≥ 0 and integers
Solver model:
x 0
y 110
z 0
P 44
Sewing time 220
Glueing time 660
Optimum solution:
x = 0, y = 110, z = 0, P = 44

orchestra answered 2 years ago
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