In: Statistics and Probability
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?
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 |