Production Problem
Production ProblemThe bicycle company Goliath is deciding on their production schedule for the next month. They produce two types of bikes, a basic version, and a premium one. They are in the enviable position that they have so many customers they will be able to sell any bike that they make. Counting just material cost, the profit per bike is EUR 175 for the basic and EUR 400 for the premium version.
To make the bikes, several production steps must be done. The following table shows informaiton on this, including the number of hours the employees in this department normally work, and the amount of time needed per department for the different types of bike.
Department
Time available
Basic
Premium
Frame
160 hours
1.2 hours
1.8 hours
Mechanical
160 hours
0.5 hours
2.7 hours
Painting
80 hours
0.25 hours
0.4 hours
To increase production, it is possible to ask employees to work overtime. However, this costs EUR 100 per hour, and is limited to 10% of the regular working hours.
(a) Formulate a linear programming model for this problem.
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