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 3 years agoRelated Solutions
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