Terrance Factory receives an order for 12000 bicycles from a customer. Each bicycle has three major components: a frameset, a seat, and a pair of wheels. The production department has to concern the availability of three resources to produce the three components. The availability of the plastic and carbon fiber are 50000 units and 30000 units, respectively. Also, the factory has 250 hours of regular manufacturing time and 70 hours of overtime that can be scheduled. Overtime involves a premium at the additional cost of $6 per hour. The information for the production is shown as follows: However, the production manager confirms that the amount of the available resources are not sufficient to meet this order. Therefore, the production manager has to get the three components from an outside supplier. The cost from the supplier and manufacturing costs for the components are summarized below. Formulate an appropriate linear programming model that would tell Terrance how to fill the order for 12000 bicycles at the minimum cost. [13 marks]

Component	plastic	Manufacturing time (minutes)	Carbon fiber
Frameset/unit	3	10	2
Seat/unit	4	6	2
Wheel(each)	2	4	1

Component	Supplier cost($)	Terrance cost($)
Frameset/unit	12	8
Seat/unit	9	6
Wheel(each)	4	2